担当区分：最終著者   記述言語：英語   掲載種別：研究論文（学術雑誌）  

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Research Association of Statistical Sciences  

Many papers have studied theoretical properties of a kernel type estimator of a distribution function. Especially mean squared errors are precisely studied. The asymptotic distribution of the estimator is also discussed, and it is easy to show asymptotic normality. In this paper, we will discuss higher order approximation of the distribution of the kernel estimator. We will obtain an Edgeworth expansion, which takes an explicit form. Assuming a bandwidth h_n=o(n^<-c>)(1/4≤c<1/2), we obtain the explicit form of the expansion with residual term o(n^<-1>). We also discuss a bias term precisely.

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER HEIDELBERG  

We derive the Edgeworth expansion for the studentized version of the kernel quantile estimator. Inverting the expansion allows us to get very accurate confidence intervals for the pth quantile under general conditions. The results are applicable in practice to improve inference for quantiles when sample sizes are moderate.

DOI： 10.1007/s10463-012-0369-6

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Research Association of Statistical Sciences  

Many papers have studied theoretical properties of a kernel density estimator. Especially mean integrated squared errors are precisely studied. The asymptotic distribution of the estimator is also discussed, and it is easy to show asymptotic normality. In this paper, we will discuss higher order approximation of the distribution of the kernel estimator. We will obtain an Edgeworth expansion, which takes an explicit form. Assuming a bandwidth h_n=O(n^<(-1)/4>), we also prove the validity of the expansion with residual term o(n^<(-3)/4>).

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER HEIDELBERG  

Using the kernel estimator of the pth quantile of a distribution brings about an improvement in comparison to the sample quantile estimator. The size and order of this improvement is revealed when studying the Edgeworth expansion of the kernel estimator. Using one more term beyond the normal approximation significantly improves the accuracy for small to moderate samples. The investigation is non- standard since the influence function of the resulting L-statistic explicitly depends on the sample size. We obtain the expansion, justify its validity and demonstrate the numerical gains in using it.

DOI： 10.1007/s10463-009-0241-5

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Research Association of Statistical Sciences  

In this paper, we obtain an asymptotic representation of the bootstrap variance estimator for a class of U-statistics. Using the representation of the estimator, we will obtain a mean squared error of the variance estimator until the order n^<-2>. Also we compare the bootstrap and the jackknife variance estimators, theoretically.

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：TAYLOR & FRANCIS INC  

Some statistics in common use take the form of a ratio of two statistics, such as sample correlation coefficient, Pearson&apos;s coefficient of variation, cumulant estimators, and so on. In this article, using an asymptotic representation of the ratio statistics, we will obtain an Edgeworth expansion and a normalizing transformation with remainder term o(n-1/2). The Edgeworth expansion is based on a Studentized ratio statistic, which is studentized by a consistent variance estimator. Applying these results to the sample correlation coefficient, we obtain the normalizing transformation and an asymptotic confidence interval of the correlation coefficient without assuming specific underlying distribution. This normalizing transformation is an extension of the Fisher&apos;s z-transformation.

DOI： 10.1080/03610920802311741

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記述言語：日本語   掲載種別：研究論文（学術雑誌）  

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Research Association of Statistical Sciences  

We obtain a stochastic approximation of a jackknife variance estimator of an L-statistic and also derive an approximation of a studentized L-statistic, in which we substitute the jackknife variance estimator. An Edgeworth expansion with remainder term o($n^-1/2$) is established for the studentized L-statistic. Using the Edgeworth expansion, we also discuss a normalizing transformation which improves the accuracy of the coverage probability of confidence interval.

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：ELSEVIER SCIENCE BV  

This paper presents discussion of properties of asymptotic confidence intervals based on a normalizing transformation and a Cornish-Fisher inversion of a studentized statistic. The normalizing transformation discussed herein removes bias, skewness and kurtosis. The Cornish-Fisher inversion is obtained from the Edgeworth expansion of the studentized statistic with residual term o(n(-1)). Asymptotic mean-squared errors and simulation results are also discussed. (c) 2004 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.jspi.2004.02.009

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Research Association of Statistical Sciences  

As an estimator of an estimable parameter, Toda and Yamato (2001) introduce Y-statistic which is a convex combination of U-statistics including V-statistic and LB-statistic. We give the Edgeworth expansions of studentized Y-statistic about the estimable parameter using a jackknife variance estimator, with remainder $ o(n^{-1}) $.

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Research Association of Statistical Sciences  

A skewness is a measure of symmetry of a distribution and appears in an Edgeworth expansion of a standardized or studentized statistic. It has been found in simulation studies that jackknife estimators of the skewness have downward biases. Fujioka and Maesono (2000) have obtained a normalizing transformation with residual term $ o(n^{-1}) $ and they pointed out that in order to construct the normalizing transformation, we need an asymptotic representation of a skewness estimator. Maesono (1998) has obtained the asymptotic representation of the jackknife skewness estimators and discussed their biases. In this paper we propose another skewness estimator of a $ U $-statistic and obtain asymptotic representations of both estimators with remainder term $ o_p(n^{-1}) $ and discuss the biases theoretically.

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：ELSEVIER SCIENCE BV  

This paper proposes a normalizing transformation which removes bias, skewness and kurtosis, simultaneously. Its convergence rate to the standard normal distribution is o(n(-1)). The transformation is polynomial and monotone. We consider a class of asymptotic U-statistics, which includes most of interesting statistics. (C) 2000 Elsevier Science B.V. All rights reserved. MSC: primary 62G20; secondary 62E20.

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：BLACKWELL PUBL LTD  

The operation of resampling from a bootstrap resample, encountered in applications of the double bootstrap, may be viewed as resampling directly from the sample but using probability weights that are proportional to the numbers of times that sample values appear in the resample. This suggests an approximate approach to double-bootstrap Monte Carlo simulation, where weighted bootstrap methods are used to circumvent much of the labour involved in compounded Monte Carlo approximation. In the case of distribution estimation or, equivalently, confidence interval calibration, the new method may be used to reduce the computational labour. Moreover, the method produces the same order of magnitude of coverage error for confidence intervals, or level error for hypothesis tests, as a full application of the double bootstrap.

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：KLUWER ACADEMIC PUBL  

In this paper we obtain asymptotic representations of several variance estimators of U-statistics and study their effects for studentizations via Edgeworth expansions. Jackknife, unbiased and Sen's variance estimators are investigated up to the order o(p)(n(-1)). Substituting these estimators to studentized U-statistics, the Edgeworth expansions with remainder term o(n(-1)) are established and inverting the expansions, the effects on confidence intervals are discussed theoretically. We also show that Hinkley's corrected jackknife variance estimator is asymptotically equivalent to the unbiased variance estimator up to the order o(p)(n(-1)).

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：THE JAPAN STATISTICAL SOCIETY  

Many numerical examples have demonstrated that the saddlepoint approximation for the cumulative distribution function of a general normalised statistic behaves better in comparison with the third order Edgeworth expansion. This effect is especially pronounced in the tails. Here we are dealing with the inverse problem of quantile evaluation. The inversion of the Lugannani-Rice approximation is compared with the Cornish-Fisher expansion both theoretically and numerically. We show in a very general setting that the expansion of the inversion of the Lugannani-Rice approximation up to third order coincides with the Cornish-Fisher expansion. Based on this, an explanation of the superiority of the former in comparison with the latter in the tails and for small samples is given. An explicit approximation of the inversion of the Lugannani-Rice formula is suggested that utilizes the information in the cumulant generating function and improves upon the Cornish-Fisher formula.

DOI： 10.14490/jjss1995.28.21

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：THE JAPAN STATISTICAL SOCIETY  

This paper studies the variance estimators for a class of U-statistics. We obtain asymptotic representations of jackknife, Hinkley's (1978) corrected jackknife, unbiased, Sen's (1960), and new variance estimators. The asymptotic mean square errors of these estimators are theoretically investigated. The Edgeworth expansions of the estimators with remainder term o(n^-1) are also established. We show that the normalized Hinkley's corrected estimator coincides with the normalized unbiased estimator up until the order n^-1/2o_p(n^-1).

DOI： 10.14490/jjss1995.28.1

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：MARCEL DEKKER INC  

Some statistics in common use take a form of a ratio of two statistics. In this paper, we will discuss asymptotic properties of the ratio statistic. We obtain an asymptotic representation of the ratio with remainder term o(p)(n(-1)) and a Edgeworth expansion with remainder term o(n(-1/2)). And as example, the asymptotic representation and the Edgeworth expansion of the jackknife skewness estimator for U-statistics are established and we discuss the biases of the skewness estimator theoretically. We also apply the result to an estimator of Pearson's coefficient of variation and the sample correlation coefficient.

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Research Association of Statistical Sciences  

It has been found in simulation studies that jackknife estimators of skewness have downward biases. In this paper we obtain asymptotic representations of the jackknife skewness estimators for $ U $-statistics with remainder term $ o_p(n^{-1}) $ and discuss the biases theoretically. Using the asymptotic representations, we also obtain Edgeworth expansions with remainder term $ o(n^{-1/2}) $.

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：ELSEVIER SCIENCE BV  

We obtain the H-decomposition of a jackknife estimator of the variance of U-statistic and derive an Edgeworth expansion with remainder term o(n(-1/2)). We also obtain an approximation of a studentized U-statistic substituting the jackknife estimator of the variance. An Edgeworth expansion with remainder term o(n(-1)) is established for the studentized U-statistic with arbitrary degree of the kernel.

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：MARCEL DEKKER INC  

In this paper we study the biases of jackknife estimators of central third moments which play an important role in improving the accuracy of the normal approximation. It has been found in simulation studies that the jackknife estimator of the skewness coefficient, into which the jackknife variance and third moment estimators are substituted, have downward biases. For the jackknife variance estimators, their asymptotic properties are precisely studied and their biases are discussed theoretically. Here we study the biases of the jackknife estimators of the central third moments for U-statistics theoretically. The results show that the biases are not always downward.

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.2206/kyushujm.50.311

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Taylor and Francis Inc.  

In this paper we discuss jackknife estimators of the variance and their corrections precisely. Shao-Wu [10] have studied a jackknife variance estimator which is based on a delete-d-original estimator. And they have proved the consistency of the delete-d jackknife variance estimator even if the original estimator is not smooth. Their results are especially useful for the jackknife estimation of the variance of the sample quantile. Whereas in the case of smooth original estimators, which include U-statistics, the delete-d jackknife variance estimator is at least as large as the delete-1 estimator which is the traditional jackknife variance estimator. Then the delete-d jackknife variance estimator has larger bias than the delete-1.

DOI： 10.1080/10485259608832687

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.14490/jjss1995.25.19

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：ELSEVIER SCIENCE BV  

The rates of convergence to the normal distribution are investigated for V- and L-statistics. We derive an inequality which gives a lower bound of the uniform distance between two distributions of the V-statistic and the normal distribution. We obtain an inequality which gives a lower bound of the uniform distance, and is meaningful in the case that the distribution of the standardized V-statistic is symmetric around the origin. Further, we also derive similar inequalities for the L-statistic. The proofs are based on Stein's method.

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：ELSEVIER SCIENCE BV  

The rates of convergence to the normal distribution are investigated for U-statistics of degree two. We derive an inequality which gives a lower bound for the uniform distance between the distribution of a U-statistic and the standard normal distribution, and which is useful in the case where the distribution of U-statistic is symmetric around the orgin. The proof is based on Stein's method.

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記述言語：日本語   掲載種別：研究論文（学術雑誌）   出版者・発行元：The Mathematical Society of Japan  

DOI： 10.11429/sugaku1947.43.205

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その他リンク： https://jlc.jst.go.jp/DN/JALC/00384238747?from=CiNii

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：ELSEVIER SCIENCE BV  

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：MARCEL DEKKER INC  

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

The rates of convergence to the normal distribution are investigated for a sum of independent random variables. Using Stein's method, we derive a lower bound of the uniform distance between two distributions of independent sum and normal. Copyright © 1989, Wiley Blackwell. All rights reserved

DOI： 10.1111/j.1467-842X.1989.tb00991.x

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

In this paper, the rates of convergence to the normal distribution are investigated for U-statistics. Using Stein’s method, we derive a lower bound of the uniform distance between the distributions of U-statistics and the standard normal distribution. © 1988, Physica-Verlag Ges.m.b.H. All rights reserved.

DOI： 10.1007/BF02613314

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：KLUWER ACADEMIC PUBL  

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：MARCEL DEKKER INC  

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担当区分：最終著者   記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：MARCEL DEKKER INC  

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：九州大学  

The asymptotic normality under the null hypothesis and also under a contiguous alternative is explored for the semi-parametric method in a multiply matched case-control study in a context of testing statistical hypothesis. The Pitman efficiency of the method is compared with the tests from the classical approach in a framework of a location and scale parameter models. It is shown that the method could lose substantial efficiency when the underlying distribution is normal.

DOI： 10.2206/kyushumfs.40.19

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その他リンク： https://jlc.jst.go.jp/DN/JALC/00297738235?from=CiNii

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：九州大学  

Over-all rank tests, for continuous data, are developed in order to combine individual test results in pairwise comparisons between cases and each of $ k $ control groups in a $ 1 $ to $ k $ matched design in case-control studies. Although the over-all-tests do not always have higher efficiencies than some tests which do not have the over-all-function, it is shown that the loss of efficiency would not be considerable.

DOI： 10.2206/kyushumfs.38.75

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その他リンク： https://jlc.jst.go.jp/DN/JALC/00300484050?from=CiNii

記述言語：日本語   著書種別：学術書

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記述言語：日本語   会議種別：口頭発表（一般）  

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記述言語：日本語   会議種別：口頭発表（招待・特別）  

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境界バイアスを修正したカーネル型分布関数推定量を利用した適合度検定の性質

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記述言語：日本語   会議種別：口頭発表（一般）  

統計的推測の重要な問題である確率点推定のカーネル型推定量の漸近平均二乗誤差を導き，その良さを理論的に示した

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記述言語：日本語   会議種別：口頭発表（一般）  

境界バイアスを修正したカーネル型分布関数推定量を利用した適合度検定の性質

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記述言語：英語   会議種別：口頭発表（一般）  

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記述言語：英語   会議種別：口頭発表（一般）  

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記述言語：英語   会議種別：口頭発表（一般）  

共通主成分分析を利用した新しい変化点探索法を提案し，実データに対する応用を行った

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記述言語：日本語   会議種別：口頭発表（一般）  

位置情報を持つ関数データに対する新しい判別法の提案を行い，実データへの適用を議論した

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記述言語：日本語   会議種別：口頭発表（一般）  

多変数関数データに対する部分空間法の構築とそれを利用した判別法の提案を行い，実データへの適用を行った．

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記述言語：日本語   会議種別：口頭発表（一般）  

共通主成分分析を利用した新しい変化点探索法を提案し，実データに対する応用を行った

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記述言語：日本語   会議種別：口頭発表（一般）  

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記述言語：英語   会議種別：口頭発表（一般）  

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