柿沢 佳秀(カキザワ ヨシヒデ) |

経済学研究院 現代経済経営部門 経済分析分野 |

教授 |

Last Updated :2022/09/26

**Bias-correction of some estimators in the INAR(1) process**ZENG Xiaoqiang, KAKIZAWA YoshihideStatistics & Probability Letters 187 1 1 - 8 2022年08月 [査読有り][通常論文]**Multivariate elliptical-based Birnbaum-Saunders kernel density estimation for nonnegative data**KAKIZAWA YoshihideJournal of Multivariate Analysis 187 1 1 - 20 2022年 [査読有り]**Recursive asymmetric kernel density estimation for nonnegative data**KAKIZAWA YoshihideJournal of Nonparametric Statistics 33 2 197 - 224 2021年 [査読有り]**A class of Birnbaum-Saunders type kernel density estimators for nonnegative data**KAKIZAWA YoshihideComputational Statistics and Data Analysis 161 1 1 - 18 2021年 [査読有り]**Higher-order bias corrections for kernel type density estimators on the unit or semi-infinite interva**IGARASHI Gaku, KAKIZAWA YoshihideJournal of Nonparametric Statistics 32 3 617 - 647 2020年 [査読有り]**Multivariate non-central Birnbaum-Saunders kernel density estimator for nonnegative data**KAKIZAWA YoshihideJournal of Statistical Planning and Inference 209 1 187 - 207 2020年 [査読有り]- IGARASHI Gaku, KAKIZAWA YoshihideComputational Statistics and Data Analysis 141 1 40 - 61 2020年01月 [査読有り][通常論文]
- Yoshihide KakizawaJOURNAL OF STATISTICAL PLANNING AND INFERENCE 193 1 117 - 135 2018年02月 [査読有り][通常論文]

The classical Birnbaum Saunders (BS) distribution haS recently been generalized in various ways to introduce flexible parametric models for nonnegative data, focusing on the parametric fitting. In this paper, a new symmetrical-based inverse/reciprocal inverse Gaussian density, through dual transformation, is applied to the context of nonparametric density estimation for nonnegative data. The beauty and importance of new density estimator lies in its general formulation via the density generator, including a log-symmetrical kernel density estimator. We provide sufficient conditions under which the proposed estimator has desirable asymptotic properties, and discuss the asymptotic comparison between the proposed estimator and the previous (normal-based) estimator. (C) 2017 Elsevier B.V. All rights reserved. - IGARASHI Gaku, KAKIZAWA YoshihideJournal of Nonparametric Statistics 30 3 598 - 639 2018年 [査読有り][通常論文]
- IGARASHI Gaku, KAKIZAWA YoshihideCommunications in Statistics: Theory and Methods 47 20 4905 - 4937 2018年 [査読有り][通常論文]
- Yoshihide Kakizawa, Gaku IgaraShiJOURNAL OF THE KOREAN STATISTICAL SOCIETY 46 2 194 - 207 2017年06月 [査読有り][通常論文]

This paper considers a varying asymmetric kernel estimation of the density f for non negative data. Regardless of f(0) = 0 or f (0) > 0, it is important to give a good varying shape/scale parameter for the inverse gamma (IGam) kernel, due to the problem of (f) over cap (0) = 0 in some existing literature. After reformulating the IGam kernel density estimator, asymptotic properties like mean, integrated squared error, mean integrated absolute error, strong consistency, and asymptotic normality are investigated in detail, under some conditions on the target density f. Simulation studies are conducted to compare the proposed IGam kernel density estimators with the existing gamma kernel density estimators. (C) 2016 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved. - Yoshihide KakizawaJOURNAL OF MULTIVARIATE ANALYSIS 153 1 98 - 120 2017年01月 [査読有り][通常論文]

Statistical inference in the presence of a nuisance parameter is often based on profile likelihood. Because it is not a genuine likelihood function, several adjustments to the profile likelihood function for eliminating score/information bias were proposed in the 1980s and 1990s, under the so-called global parameter orthogonality. On the basis of Stern's (1997) adjusted profile likelihood, which is applicable even without the global parameter orthogonality, we discuss higher-order average local power properties after several Bartlett-type adjustments. It turns out that Rao's statistic arising from Stern's adjusted profile likelihood continues to enjoy desirable average local power properties, as in the ordinary likelihood inference. We also investigate, using a simulation, the performance of Rao's test, compared with the likelihood ratio test and Wald's test. (C) 2016 Elsevier Inc. All rights reserved. - Yoshihide KakizawaSTATISTICS & PROBABILITY LETTERS 110 1 162 - 168 2016年03月 [査読有り][通常論文]

We present the formula for a certain integral with respect to multivariate Hermite polynomials. Such integrals are used for deriving higher-order local power functions of asymptotically chi-squared tests. As an example, we provide asymptotic expansion for the local power function of Rao's score test. (C) 2015 Elsevier B.V. All rights reserved. - Yoshihide KakizawaJOURNAL OF MULTIVARIATE ANALYSIS 140 1 99 - 112 2015年09月 [査読有り][通常論文]

The Bartlett-type adjustment is a higher-order asymptotic method for improving the chi-squared approximation to the null distributions of various test statistics, which ensures that the resulting test has size alpha + o(N-1), where 0 < alpha < 1 is the significance level and N is the sample size. We continue our recent works on the third-order average local power properties of several Bartlett-type adjusted tests. Strengthening the results in the 1990s, the third-order optimality of the adjusted Rao test in a sense has been established even if both the interest parameter and the nuisance parameter are multi-dimensional. We briefly discuss adjusted profile likelihood, inference for handling the nuisance parameter. (C) 2015 Elsevier Inc. All rights reserved. - Gaku Igarashi, Yoshihide KakizawaJOURNAL OF STATISTICAL PLANNING AND INFERENCE 159 1 37 - 63 2015年04月 [査読有り][通常論文]

Several asymmetric kernel (AK) estimators of a density with support [0, infinity) have been suggested in the recent fifteen years. In this paper, additive and nonnegative bias correction techniques, originally developed for the standard kernel estimator, are applied to some AK estimators when the underlying density has a fourth order derivative. The major contribution is to study asymptotic properties of new AK estimators corresponding to the limits of improved estimators. Simulation studies are conducted to illustrate the finite sample performance of the proposed estimators. (C) 2014 Elsevier B.V. All rights reserved. - Gaku Igarashi, Yoshihide KakizawaSTATISTICS & PROBABILITY LETTERS 84 1 235 - 246 2014年01月 [査読有り][通常論文]

We reveal the boundary bias problem of Birnbaum-Saunders, inverse Gaussian, and reciprocal inverse Gaussian kernel estimators (Jin and Kawczak, 2003; Scaillet, 2004) and re-formulate these estimators to solve the problem. We investigate asymptotic properties of a new class of asymmetric kernel estimators. (C) 2013 Elsevier B.V. All rights reserved. - Gaku Igarashi, Yoshihide KakizawaJOURNAL OF NONPARAMETRIC STATISTICS 26 1 61 - 84 2014年01月 [査読有り][通常論文]
- Yoshihide KakizawaJOURNAL OF MULTIVARIATE ANALYSIS 114 1 303 - 317 2013年02月 [査読有り][通常論文]

This paper addresses, for a composite hypothesis about a subvector of the parameters in the parametric model, the issues posed by Rao and Mukerjee (1995) [22] and Li (2001) [14] on the power under a sequence of local alternatives. It is shown that a partially adjusted test statistic in a class of test statistics is equally sensitive (up to the third-order) to the change of the nuisance parameters. However, there exist infinitely many ways for improving the chi-squared approximation to the null distribution, which reveal, in general, the non-equivalence of the resulting third-order point-by-point local powers. To make a definitive conclusion, the average local power is then considered, from which the third-order asymptotic optimality of the Bartlett-type adjusted Rao test can be also established. (C) 2012 Elsevier Inc. All rights reserved. - Yoshihide KakizawaJournal of Time Series Analysis 34 6 691 - 716 2013年 [査読有り][通常論文]

This paper is concerned with a version of empirical likelihood method for spectral restrictions, which handles stationary time series data via the frequency domain approach. The asymptotic properties of frequency domain generalized empirical likelihood are studied for either strictly stationary processes with vanishing cumulant spectral density function of order 4 or linear processes generated by iid innovations with possibly non-zero fourth order cumulant. Several statistics for testing parametric restrictions, over-identified spectral restrictions, and additional spectral restrictions are shown to have the limiting chi-squared distributions. Some numerical results are presented to investigate the finite sample performance of the proposed procedures. © 2013 John Wiley & Sons, Ltd. - Yoshihide KakizawaSTATISTICS & PROBABILITY LETTERS 82 11 2008 - 2016 2012年11月 [査読有り][通常論文]

The Bartlett-type adjustment is a higher-order asymptotic method for reducing the errors of the chi-squared approximations to the null distributions of various test statistics, which ensures that the resulting test has size alpha + o(N-1), where 0 < alpha < 1 is the significance level and N is the sample size. Recently, Kakizawa (2012) has revisited the Chandra-Mukerjee/Taniguchi adjustments in a unified way, since Chandra and Mukerjee (1991) and Taniguchi (1991b) originally considered the test of the simple null hypothesis, except for Mukerjee (1992). This paper considers a generalization of the adjustment due to Cordeiro and Ferrari (1991). (C) 2012 Elsevier B.V. All rights reserved. - Yoshihide KakizawaJOURNAL OF MULTIVARIATE ANALYSIS 107 1 141 - 161 2012年05月 [査読有り][通常論文]

The Bartlett-type adjustment is a higher-order asymptotic method for improving the chi-squared approximation to the null distributions of various test statistics. Though three influential papers were published in 1991-Chandra and Mukerjee (1991) [8], Cordeiro and Ferrari (1991) [12] and Taniguchi (1991) [36] in alphabetical order, the only CF-approach has been frequently applied in the literature during the last two decades, provided that asymptotic expansion for the null distribution of a given test statistic is available. Revisiting the CM/T-approaches developed in the absence of a nuisance parameter, this paper suggests general adjustments for a class of test statistics that includes, in particular, the likelihood ratio, Rao's and Wald's test statistics in the presence of a nuisance parameter. (C) 2012 Elsevier Inc. All rights reserved. - Yoshihide KakizawaCOMMUNICATIONS IN STATISTICS-THEORY AND METHODS 41 20 3676 - 3691 2012年 [査読有り][通常論文]

The second-order local powers of a broad class of asymptotic chi-squared tests are considered in a composite case where both the parameter of interest and the nuisance parameter are possibly multidimensional for which no assumption has been made regarding global parametric orthogonality or curved exponentiality. The main result is that the second-order (point-by-point) local power identity holds if approximate third cumulants of a square-root version of the (modified) test statistic in the class vanish up to the second-order, which is an extension of Kakizawa (2010a) in the absence of the nuisance parameter. It is also shown that in the presence of the nuisance parameter, such a third cumulant condition does not always imply the second-order local unbiasedness of the resulting test. Then, the adjusted likelihood ratio test by Mukerjee (1993b) can be interpreted as the second-order local unbiased modification after applying the third cumulant condition. - Yoshihide KakizawaSTATISTICS & PROBABILITY LETTERS 81 8 1245 - 1255 2011年08月 [査読有り][通常論文]

The Bartlett adjustment, being a simple adjustment through division by the expected value of the test statistic, is commonly used as a general statistical tool to reduce the error of the chi-squared approximation of parametric/empirical likelihood ratio (LR/ELR) test statistic. In this paper, some improved test statistics in the additive forms are presented, whose errors of the chi-squared approximation are o(N(-1)), as in the case of the traditional multiplicative Bartlett adjustment, where N is the sample size. By deriving the N(-1)-difference of the power functions of two tests under a sequence of local alternatives, it is shown that none of several adjustments of the LR/ELR test statistic is uniformly superior. The results are numerically illustrated on specific examples. (C) 2011 Elsevier B.V. All rights reserved. - Yoshihide KakizawaSTATISTICAL METHODOLOGY 8 2 136 - 153 2011年03月 [査読有り][通常論文]

We propose a rescaled generalized Bernstein polynomial for approximating any continuous function defined on the closed interval [0, Delta]. Using this polynomial which is of degree m - 1 and depends on the additional parameter s(m), we consider the nonparametric density estimation for two contexts. One is that of a spectral density function of a real-valued stationary process, and the other is that of a probability density function with support [0, 1]. Our density estimators can be interpreted as a convex combination of the uniform kernel density estimators at m points, whose coefficients are probabilities of the binomial random variable with parameters (m - 1, x/Delta), depending on the location x is an element of [0, Delta] where the density estimation is made. We examine in detail the asymptotic bias, variance and mean integrated squared error for a class of our density estimators under the framework where m is an element of N tends to infinity in some way as the sample size tends to infinity. Using a specific data set, we also include a numerical comparison between our density estimators and the Bernstein-Kantorovich polynomial density estimator obtained through the cross-validation method. (C) 2010 Elsevier BM. All rights reserved. - Yoshihide KakizawaJOURNAL OF MULTIVARIATE ANALYSIS 101 7 1638 - 1655 2010年08月 [査読有り][通常論文]

Considering some Bartlett-type adjusted tests for a simple hypothesis about a multidimensional parameter, this paper clarifies similarities and dissimilarities with the one-parameter case developed in the 1990s, where a major emphasis is put on the issue posed by Rao and Mukerjee [C.R. Rao, R. Mukerjee, Comparison of Bartlett-type adjustments for the efficient score statistic, J. Statist. Plann. Inference 46 (1995) 137-146] on the power under a sequence of local alternatives. Not surprisingly, there is an infinite number of adjustments which extend Chandra-Mukerjee and Taniguchi approaches to the multiparameter case. Revisiting their ideas, this paper presents four specific cases (type K, K = 0, 1, 2, 3) and gives a sufficient condition under which our generalized adjustment for each case is uniquely determined, where type 0 is a counterpart of Chandra and Mukerjee's original proposal for Rao's test statistic, whereas the latter three types are introduced as double adjustments related to the Cordeiro and Ferrari approach. lithe adjustment of type 1 is made instead of type K, K = 0, 2, 3, it is shown that Chandra and Mukerjee's approach is equivalent to Taniguchi's approach in terms of the third-order local power. The same is partially true for type 0, depending on the model under consideration. However, the adjustments of type K, K = 2, 3, reveal, in general, the non-equivalence of these two approaches in terms of the third-order local power. (C) 2010 Elsevier Inc. All rights reserved. - Yoshihide KakizawaCOMMUNICATIONS IN STATISTICS-THEORY AND METHODS 39 8-9 1424 - 1436 2010年 [査読有り][通常論文]

The second-order local power of a class of tests for a simple hypothesis about a multi-dimensional unknown parameter is considered. It turns out that the test procedure adjusted differently from Mukerjee (1990a) has the identical second-order local power without making use of the average power criterion. The basic principle behind the power identity is that approximate third-order cumulants of the modified square-root version of the test statistic vanish. This represents a substantial extension of the second-order asymptotic results of tests in the 1980s and early 1990s. - Toshiya Iwashita, Yoshihide Kakizawa, Tatsuki Inoue, Takashi SeoSTATISTICS & PROBABILITY LETTERS 79 18 1935 - 1942 2009年09月 [査読有り][通常論文]

An asymptotic expansion of the distribution of Student's t type statistic based on the multivariate standardized or studentized sample mean vector is obtained by making use of an Edgeworth expansion up to the order O(N(-2)), where N is sample size and Student's t type transformation is defined by T(alpha)(X) = (p - 1)(1/2)alpha'X(parallel to X parallel to(2) - (alpha'X)(2))(-1/2) for any alpha is an element of R(p), alpha'alpha = 1. It turns out that at t-approximation to Student's t type statistic based on the studentized sample mean vector has the error o(N(-l)), if a certain spherical population has at least 4(l + 1)th moment, where l = 0, 1, 2. Some numerical experiments are also conducted to evaluate the accuracy of the result. (C) 2009 Elsevier B.V. All rights reserved. - Yoshihide KakizawaANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 61 1 1 - 26 2009年03月 [査読有り][通常論文]

The limiting joint distribution of correlated Hotelling's T(2) statistics associated with multiple comparisons with a control in multivariate one-way layout model is a multivariate central nonsingular chi-square distribution with one-factorial correlation matrix, which has the distribution function expressed in a closed form as an integral of a product of noncentral chi-square distribution functions with respect to a central chi-square density function. For pairwise comparisons, it is a multivariate central singular chi-square distribution whose distribution function is generally intricate. To overcome the complexity of the (exact or asymptotic) distribution theory of T(max)(2)-type statistics appeared in simultaneous confidence intervals of mean vectors, improved Bonferroni-type inequalities are applied to construct asymptotically conservative simultaneous confidence intervals for pairwise comparisons as well as comparisons with a control. - Yoshihide KakizawaJOURNAL OF MULTIVARIATE ANALYSIS 100 3 473 - 496 2009年03月 [査読有り][通常論文]

The purpose of this paper is, in multivariate linear regression model (Part I) and GMANOVA model (Part II), to investigate the effect of nonnomality upon the nonnull distributions of some multivariate test Statistics under normality. It is shown that whatever the underlying distributions, the difference of local powers up to order N(-1) after either Bartlett's type adjustment or Cornish-Fisher's type size adjustment under nonnormality coincides with that in Anderson [An Introduction to Multivariate Statistical Analysis, 2nd ed. and 3rd ed., Wiley, New York, 1984, 20031 under normality. The derivation of asymptotic expansions is based oil the differential operator associated with the multivariate linear regression model under general distributions. The performance of higher-order results in finite samples, including monotone Bartlett's type adjusment and monotone Cornish-Fisher's type size adjustment, is examined using simulation studies. (c) 2008 Elsevier Inc. All rights reserved. - Yoshihide Kakizawa, Toshiya IwashitaJOURNAL OF STATISTICAL PLANNING AND INFERENCE 138 11 3379 - 3404 2008年11月 [査読有り][通常論文]

This paper provides a powerful method for obtaining an asymptotic expansion for the expectation of a function of the normalized sample mean vector N-1/2(U) over bar and the sample covariance matrix S-U under general distributions, without using the Edgeworth expansion of N-1/2 4 I U, and N-1/2 Sigma(N)(i=1) vech(UiU'(i) - Sigma). It is shown that asymptotic expansions of the nonnull distributions of some multivariate test statistics on mean vectors under general distributions are derived in a unified way, by finding the differential operator associated with the expectation according to situations under consideration. Unlike Kano [1995. An asymptotic expansion of the distribution of Hotelling's T-2-statistic under general distributions. Amer. J. Math. Manage. Sci. 15, 317-341] and Fujikoshi [1997. An asymptotic expansion for the distribution of Hotelling's T-2-statistic under nonnormality. J. Multivariate Anal. 61, 187-193], our routine for getting asymptotic expansions is to collect some patterned derivatives, without constructing the Edgeworth expansion of some basic statistics. In this sense, our approach seems to be more convenient, at least, for Hotelling's T-2-type statistics and other related statistics on mean vectors. (C) 2008 Elsevier B.V. All rights reserved. - Yoshihide KakizawaSTATISTICS & PROBABILITY LETTERS 78 11 1328 - 1338 2008年08月 [査読有り][通常論文]

This paper presents several statistics appearing in multiple comparisons of heteroscedastic multivariate populations. Due to the very slow convergence of these statistics to their limiting distributions, the large sample Bonferroni or DL-based procedures reveal poor coverage probabilities even in the normal case. Thus, the second-order asymptotic expansions with estimated cumulants are applied to improve their coverage probabilities. A large simulation study illustrates the performance of the second-order corrected procedures. (C) 2007 Elsevier B.V. All rights reserved. - Yoshihide Kakizawa, Toshiya IwashitaJOURNAL OF MULTIVARIATE ANALYSIS 99 6 1128 - 1153 2008年07月 [査読有り][通常論文]

The purpose of this paper is to investigate the effect of nonnormality upon the nonnull distributions of some MANOVA test statistics under normality. It is shown that whatever the underlying distributions, the difference of the local powers up to order N-1 (N is the total number of observations) after either Bartlett's type adjustment or Cornish-Fisher's type adjustment under normormality coincides with that in Anderson [An Introduction to Multivariate Statistical Analysis, second ed., 1984 and third ed., 2003, Wiley, New York] under normality. The performance of higher-order results in finite samples is examined using simulation studies. (C) 2007 Elsevier Inc. All rights reserved. - Yoshihide KakizawaCOMMUNICATIONS IN STATISTICS-THEORY AND METHODS 37 1 97 - 120 2008年 [査読有り][通常論文]

This article presents asymptotic expansions for the joint characteristic function and the joint distribution of correlated but asymptotically independent (i.e., quasi-independent) Hotelling's T-2 statistics under nonnormality, which is an extension of Fujikoshi and Seo (1999) under normality. The derivation is based on the differential operator developed by Kakizawa and Iwashita (2005a). Also, asymptotic expansions for the distributions of maximum and sum of quasi-independent Hotelling's T-2 statistics are derived in order to construct simultaneous confidence intervals of mean vectors in the one-way layout model. **多変量解析における漸近展開: 微分作用素の使用の観点から**柿沢佳秀, 岩下登志也国際数理科学協会会報 56 14 - 25 2008年 [査読無し][通常論文]- KAKIZAWA YoshihideJournal of the Japan Statistical Society 37 2 253 - 283 THE JAPAN STATISTICAL SOCIETY 2007年12月 [査読有り][通常論文]

This paper deals with a test of equality of mean vectors of several heteroscedastic multivariate populations. We derive not only the asymptotic expansion up to N^<-1> of the nonnull distribution of James's (1954) statistic, but also those of two corrected statistics due to Cordeiro and Ferrari (1991) and Kakizawa (1996). The derivation we considered here is based on the differential operator method developed in Kakizawa and Iwashita (2005). - Yoshihide KakizawaJOURNAL OF MULTIVARIATE ANALYSIS 98 5 992 - 1017 2007年05月 [査読有り][通常論文]

Moderate deviations limit theorem is proved for quadratic forms in zero-mean Gaussian stationary processes. Two particular cases are the cumulative periodogram and the kernel spectral density estimator. We also derive the exponential decay of moderate deviation probabilities of goodness-of-fit tests for the spectral density and then discuss intermediate asymptotic efficiencies of tests. (c) 2006 Elsevier Inc. All rights reserved. - KAKIZAWA YoshihideSUT Journal of Mathematics 42 1 59 - 96 2006年06月 [査読有り][通常論文]
- Y KakizawaJOURNAL OF TIME SERIES ANALYSIS 27 2 253 - 287 2006年03月 [査読有り][通常論文]

We consider an application of Bernstein polynomials for estimating a spectral density of a stationary process. The resulting estimator can be interpreted as a convex combination of the (Daniell) kernel spectral density estimators at m points, the coefficients of which are probabilities of the binomial distribution bin(m - 1, vertical bar lambda vertical bar/pi), lambda is an element of Pi equivalent to [-pi, pi] being the frequency where the spectral density estimation is made. Several asymptotic properties are investigated under conditions of the degree m. We also discuss methods of data-driven choice of the degree m. For a comparison with the ordinary kernel method, a Monte Carlo simulation illustrates our methodology and examines its performance in small sample. - Y KakizawaJOURNAL OF NONPARAMETRIC STATISTICS 17 6 745 - 764 2005年09月 [査読有り][通常論文]

The large deviation result is proved for two functionals of the empirical spectral process in zero-mean Gaussian stationary processes. As a statistical application, we deal with the Bahadur asymptotic efficiencies of two statistics for testing H: f(1) = f (specified), which are spectral analogue to the Kolmogorov-Smirnov (KS) and Kuiper statistics for testing hypothesis about distribution function in the iid setting. It is shown that the Kuiper type statistic is superior to the KS type statistic in terms of the Bahadur exact slope. We also discuss the a (>= 2)-sample problem. Especially, for the two-sample problem, we investigate the Bahadur asymptotic efficiencies of several statistics for testing not only the goodness-of-fit hypothesis H-1: f(1) = f(2) = f (specified) but also the homogeneity hypothesis H-2: f(1) = f(2) (unspecified). - Y KakizawaJOURNAL OF NONPARAMETRIC STATISTICS 16 5 709 - 729 2004年10月 [査読有り][通常論文]

We consider an application of Bernstein polynomials for estimating a density function with support [0, 1 ]. Two classes of estimators proposed in this article are interpreted as a linear combination of (boundary) kernel estimators at in or m + 1 points, whose coefficients are probabilities of the binomial distribution Bin(m - 1, x) or Bin(m, x), x being the position where the density estimation is made. It is shown that our estimators are free of boundary bias and achieve the convergence rate of n(-4/5) for the mean integrated squared error. Many estimators remain nonnegative, which are comparable with Chen's variable [Chen, S. X. (1999). Beta kernel estimators for density functions. Computational Statistics & Data Analysis, 31, 131-145.] (boundary) beta kernel estimators. Our first class of stimators based on the uniform kernel with boundary modification includes Vitale's estimator [Vitale, R. A. (1975). A Bernstein polynomial approach to density function estimation. In: Puri, M. L. (Ed.), Statistical Inference and Related Topics, Vol. 2. Academic Press, New York, pp. 87-99.] as a special cage, and some estimators in this subclass are superior to Chen's first estimator in terms of the asymptotic mean integrated squared error. Further, three estimators that are not only superior to Vitale's estimator but also equivalent to Chen's second estimator are proposed by using the Bernstein polynomial approach. - KAKIZAWA YoshihideJournal of the Japan Statistical Society 32 2 209 - 237 THE JAPAN STATISTICAL SOCIETY 2002年12月 [査読有り][通常論文]

This paper shows the validity of the (arbitrary) higher order Edgeworth expansion for the distribution of estimators of the coefficient parameter θ∈ (-1,1) in the AR(1) process {X_t} with a possibly nonzero initial value X_0 = x. The stationary case of X_0～N(0, 1/(1 - θ^2)) is also treated. - KAKIZAWA YoshihideSankhya, A 64 1 16 - 41 2002年02月 [査読有り][通常論文]
- Y KakizawaSTATISTICA SINICA 10 1 297 - 315 2000年01月 [査読有り][通常論文]

Global optimality of likelihood ratio test statistics is well-known in the Bahadur sense. In this paper the behaviors of Rao and Wald statistics (R-n and W-n) for testing theta = theta(o) are studied. It turns out that at alternative theta(o) + epsilon, the Bahadur slopes of these two statistics for the one-sided case are identical up to order epsilon(4), while for the two-sided case, they are identical only up to order epsilon(2), in general i.i.d. models and Gaussian stationary processes. We obtain the second (first-) order Bahadur efficiency of R-n and W-n for the one- (two-) sided case. The third-order Bahadur efficiency depends on the statistical curvature. Two concrete examples are given. One is a curved exponential family, and the other is a Gaussian AR(1) process. The latter provides an example that the epsilon(5)-term of the Bahadur slope of R-n for the one-sided case is different from that of W-n. - Y KakizawaSTOCHASTIC PROCESSES AND THEIR APPLICATIONS 85 1 29 - 44 2000年01月 [査読有り][通常論文]

In this paper the maximum likelihood and quasi-maximum likelihood estimators of a spectral parameter of a mean zero Gaussian stationary process are shown to be asymptotically efficient in the sense of Bahadur under appropriate conditions. In order to obtain exponential convergence rates of tail probabilities of these estimators, a basic result on large deviation probability of certain quadratic form is proved by using several asymptotic properties of Toeplitz matrices. It turns out that the exponential convergence rates of the MLE and qMLE are identical, which depend on the statistical curvature of Gaussian stationary process. (C) 2000 Elsevier Science B.V. All rights reserved. MSG: Primary 62F10; 62F12; 62M10; Secondary 62F03; 62F05. - KAKIZAWA YoshihideJournal of Time Series Analysis 20 3 343 - 359 1999年05月 [査読有り][通常論文]
- Yoshihide KakizawaJournal of Time Series Analysis 20 5 551 - 558 1999年 [査読有り][通常論文]

In this note certain results obtained by Porat (J. Time Ser. Anal. 8 (1987), 205-20) and Kakizawa and Taniguchi (J. Time Ser. Anal. 15 (1994), 303-11) concerning the asymptotic efficiency of sample autocovariances of a zero-mean Gaussian stationary process are extended to the case of w-vector processes. It is shown that, for Gaussian vector AR(p) processes, the sample autocovariance matrix at lag k is asymptotically efficient if 0 ≤ k ≤ p. Further, none of the sample autocovariance matrices is asymptotically efficient for Gaussian vector MA(q) processes. - Y KakizawaSTATISTICS & PROBABILITY LETTERS 38 4 355 - 362 1998年07月 [査読有り][通常論文]

A closed-form expression for the exponential rate of an estimator in the Gaussian AR(1) process is obtained. This shows that the exponential rates of several famous estimators are all identical. Further it is shown that mean-correction does not affect the large deviation asymptotics. (C) 1998 Elsevier Science B.V. All rights reserved. - T Sato, Y Kakizawa, M TaniguchiAUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS 40 1 17 - 29 1998年03月 [査読有り][通常論文]

This paper discusses the large deviation principle of several important statistics for short- and long-memory Gaussian processes. First, large deviation theorems for the log-likelihood ratio and quadratic forms for a short-memory Gaussian process with mean function are proved. Their asymptotics are described by the large deviation rate functions. Since they are complicated, they are numerically evaluated and illustrated using the Maple V system (Char et al., 1991a,b). Second, the large deviation theorem of the log-likelihood ratio statistic for a long-memory Gaussian process with constant mean is proved. The asymptotics of the long-memory case differ greatly from those of the short-memory case. The maximum likelihood estimator of a spectral parameter for a short-memory Gaussian stationary process is asymptotically efficient in the sense of Bahadur. - Y Kakizawa, RH Shumway, M TaniguchiJOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 93 441 328 - 340 1998年03月 [査読有り][通常論文]

Minimum discrimination information provides a useful generalization of likelihood methodology for classification and clustering of multivariate time series. Discrimination between different classes of multivariate time series that can be characterized by differing covariance or spectral structures is of importance in applications occurring in the analysis of geophysical and medical time series data. For discrimination between such multivariate series, Kullback-Leibler discrimination information and the Chernoff information measure are developed for the multivariate non-Gaussian case. Asymptotic error rates and limiting distributions are given for a generalized spectral disparity measure that includes the foregoing criteria as special cases. Applications to problems of clustering and classifying earthquakes and mining explosions are given. - Y KakizawaJOURNAL OF STATISTICAL PLANNING AND INFERENCE 65 2 269 - 280 1997年12月 [査読有り][通常論文]

This paper deals with Bartlett-type adjustment which makes all the terms up to order n(-k) in the asymptotic expansion vanish, where k is an integer k greater than or equal to 1 and n depends on the sample size. Extending Cordeiro and Ferrari (1991, Biometrika, 78, 573-582) for the case of k = 1, we derive a general formula of the kth-order Bartlett-type adjustment for the test statistic whose kth-order asymptotic expansion of the distribution is given by a finite linear combination of chi-squared distribution with suitable degrees of freedom. Two examples of the second-order Bartlett-type adjustment are given. We also elucidate the connection between Bartlett-type adjustment and Cornish-Fisher expansion. (C) 1997 Elsevier Science B.V. - KAKIZAWA YoshihideJournal of the Japan Statistical Society 27 1 19 - 35 日本統計学会 1997年06月 [査読有り][通常論文]
- Y KakizawaSTATISTICS & PROBABILITY LETTERS 33 3 225 - 234 1997年05月 [査読有り][通常論文]

Statistical inference for stationary time series is often based on the maximum likelihood principle, i.e., the maximization of the (quasi) likelihood of observations derived on Gaussian assumptions, although no such distributional assumptions are made. Zn this paper, we define the disparity measure between spectral density matrices and introduce the minimum distance principle for parameter estimation and hypothesis testing in spectral analysis of stationary vector time series. - Y KakizawaBIOMETRIKA 83 4 923 - 927 1996年12月 [査読有り][通常論文]

Suppose that the null distribution function of some test statistic S = S-n is expanded in terms of chi(2) distributions. In this paper we provide a method for finding a 'monotone' transformation T(x) such that T(S) has chi-squared distribution to order n(-k). This technique is applied to the special case of Hotelling's T-2-statistic. - Yoshihide KakizawaJournal of Nonparametric Statistics 7 2 187 - 203 1996年 [査読有り][通常論文]

This paper is concerned with spectral discrimination for non-Gaussian vector stationary time series. The usual discriminant rule is to maximize the (quasi) likelihood of observations derived on Gaussian assumptions, although no such distributional assumptions are made. In this paper, we introduce an alternative approach based on the disparity measure between spectral density matrices. - KAKIZAWA YoshihideJournal of the Japan Statistical Society 26 2 161 - 172 THE JAPAN STATISTICAL SOCIETY 1996年 [査読有り][通常論文]

This paper deals with the density for a class of estimators _??__{c1 c2}(*c*_{1},*c*_{2}≥0) in Gaussian AR (1) process. Here _??__{c1 c2}includes various estimators if the constants*c*_{1}and*c*_{2}are specified appropriately. Applying the saddlepoint method to the general formula by Geary [5], the density of _??__{c1 c2}is approximated. Although Phillips [14] pointed out that the saddlepoint density is undefined in a substantial part of the tails, we elucidate that the resulting approximation is always defined if*c*_{1}and*c*_{2}are appropriately chosen. Some numerical comparisons are made among the Edgeworth approximation, the saddlepoint approximation, and the exact distribution for _??__{1/2, 1/2}. We also approximate the density for the mean corrected estmator _??__{c1 c2}. - KAKIZAWA YoshihideJournal of Time Series Analysis 17 4 367 - 377 1996年 [査読有り][通常論文]
**Discriminant analysis for time series : parametric and nonparametric approach**KAKIZAWA YoshihideRIMS Kokyuroku 916 149 - 168 1995年 [査読無し][通常論文]- KAKIZAWA Yoshihide, TANIGUCHI MasanobuJournal of the Japan Statistical Society 24 2 109 - 119 1994年 [査読有り][通常論文]
- Yoshihide Kakizawa, Masanobu TaniguchiJournal of Time Series Analysis 15 3 303 - 311 1994年 [査読有り][通常論文]

Abstract. This paper deals with the asymptotic efficiency of the sample autocovariances of a Gaussian stationary process. The asymptotic variance of the sample autocovariances and the Cramer–Rao bound are expressed as the integrals of the spectral density and its derivative. We say that the sample autocovariances are asymptotically efficient if the asymptotic variance and the Cramer–Rao bound are identical. In terms of the spectral density we give a necessary and sufficient condition that they are asymptotically efficient. This condition is easy to check for various spectra. Copyright © 1994, Wiley Blackwell. All rights reserved

- TANIGUCHI Masanobu, KAKIZAWA Yoshihide
**Asymptotic Theory of Statistical Inference for Time Series**

Springer 2000年 (ISBN: 0387950397)

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