著者

Yutaka Kano

出版者

THE JAPAN STATISTICAL SOCIETY

雑誌

JOURNAL OF THE JAPAN STATISTICAL SOCIETY (ISSN:18822754)

巻号頁・発行日

vol.26, no.1, pp.101-117, 1996 (Released:2009-01-22)

参考文献数

43

被引用文献数

1 1

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Takeuchi [37], Takeuchi and Akahira [38] and Pfanzagl [27] among others proved that any first-order efficient estimators are second-order efficient. Many other authors e. g., Ghosh [15], have conjectured that any third-order efficient estimators are also fourth-order efficient. Based on the concentration probability of estimators about a true parameter, this paper gives a positive answer to the conjecture in a curved exponential family with multi-structural parameters. It is seen that choice of bias-correction factors is critical.

著者

Ekkehart Schlicht

出版者

THE JAPAN STATISTICAL SOCIETY

雑誌

JOURNAL OF THE JAPAN STATISTICAL SOCIETY (ISSN:18822754)

巻号頁・発行日

vol.35, no.1, pp.99-119, 2005 (Released:2006-01-19)

参考文献数

10

被引用文献数

34 40

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This note gives a statistical description of the Hodrick-Prescott Filter (1997), originally proposed by Leser (1961). A maximum-likelihood estimator is derived and a related moments estimator is proposed that has a straightforward intuitive interpretation and coincides with the maximum-likelihood estimator for long time series. The method is illustrated by an application and several simulations. The statistical treatment in the state-space tradition implies some scepticism regarding the interpretation in terms of low-frequency filtering.

著者

辻村 江太郎

出版者

一般社団法人 日本統計学会

雑誌

JOURNAL OF THE JAPAN STATISTICAL SOCIETY (ISSN:03895602)

巻号頁・発行日

vol.21, no.3, pp.317-321,264, 1992

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日本は世界でも有数な統計大国である.短期,中期,長期の統計資料が国民の生活全体をカバーしている.この豊富な資料を活用するには,国の経済のあり方についての哲学的判断と経済学的判断が重要である.統計では, 1987年から91年にかけて実質経済成長率が当初の政府見通しより大きくなっており,労働の需給状況についても失業率が政府見通しより小さくなっている.この統計は真実を反映しているが,それを成長率が高すぎると読むか,好ましい成長率の中で労働力が不足していると読むかは哲学的判断による.一方今回の景気上昇の中で,恐れていたインフレ・狂乱物価が統計に現れなかったのは何故か,という疑問が出されていて,経済学者が解答を出せないという局面があった.しかしよく考えてみると,それは地価の上昇が物価指数に含まれていなかったためで,表面下では大変激しい物価上昇が起きていたのである.これは経済学的判断の盲点であった.

著者

Ngai Hang Yury A. Kutoyants

出版者

日本統計学会

雑誌

JOURNAL OF THE JAPAN STATISTICAL SOCIETY (ISSN:18822754)

巻号頁・発行日

vol.40, no.2, pp.277-303, 2010-03-22 (Released:2011-09-22)

参考文献数

36

被引用文献数

2 3

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In this article, several important problems of threshold estimation in a Bayesian framework for nonlinear time series models are discussed. The paper starts with the issue of calculating the maximum likelihood and the Bayesian estimators for threshold autoregressive models. It turns out that the asymptotic efficiency of the Bayesian estimators in this type of singular estimation problems is superior than the maximum likelihood estimators. To illustrate the properties of these estimators and to explain the proposed method, the paper begins with the study of a linear threshold autoregressive model with i.i.d. Gaussian noise. The paper then extends the idea to other nonlinear and non-Gaussian models and illustrates the paradigm of limiting likelihood ratio, which is applicable to a much wider class of nonlinear models. The article also investigates the robustness issue and the possibility of restricting the observation window by narrow bands, which allows one to obtain asymptotically efficient estimators. Finally, the paper indicates how these results can be generalized from a TAR(1) model to a higher-order TAR(p) model with multiple thresholds. The paper concludes with a discussion of other related problems and illustrates the methodology by numerical simulations.

著者

Sato Michikazu Akahira Masafumi

出版者

日本統計学会

雑誌

Journal of the Japan Statistical Society (ISSN:03895602)

巻号頁・発行日

vol.25, no.2, pp.151-158, 1995

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This paper presents lower bounds for the minimax risk under quadraticloss, derived from information inequalities for the Bayes risk obtained byBorovkov and Sakhanienko, Brown and Gajek. In addition, admissibilityof a minimax estimator is discussed, and we provide examples which illustratethat they are good bounds.

著者

Akahira Masafumi Torigoe Norio

出版者

日本統計学会

雑誌

Journal of the Japan Statistical Society (ISSN:03895602)

巻号頁・発行日

vol.28, no.1, pp.45-57, 1998

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A new higher order approximation formula for a percentage point of thedistribution of the sample correlation coefficient is given up to the order O( n-1),using the Cornish-Fisher expansion for the statistic based on a linear combinationof a normal random variable and chi-random variables. The numerical comparisonof the formula with others shows that it dominates the others and gives almostprecise values in various cases even for the size n= 10 of sample.

著者

Kawai Shinichi Akahira Masafumi

出版者

日本統計学会

雑誌

Journal of the Japan Statistical Society (ISSN:03895602)

巻号頁・発行日

vol.24, no.2, pp.141-150, 1994

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In some regression model, the mean square' errors of a ratio estimator, a groupedjackknife estimator, and an estimator based on the least square estimators (LSEs) areobtained and compared up to the order O(n-3), where n is the size of the sample. Thebias-adjusted ratio estimator and the jackknife estimator are also compared up to theorder O(n-3). Then it is concluded that the estimator based on the LSEs is an asymptoticallybetter estimator of ratio up to the order o (n-3).Some examples are given.

著者

Akahira Masafumi Kawai Shinichi

出版者

日本統計学会

雑誌

Journal of the Japan Statistical Society (ISSN:03895602)

巻号頁・発行日

vol.20, no.2, pp.149-157, 1990

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In some regression model, the minimum (asymptotic) variance estimator of a ratiois discussed for some class of linear combinations of ratio estimators, and the jackknifeprocedure is considered. It is seen that the grouped jackknife estimator is optimal inthe sense that it has asymptotically the minimum variance in the class. Higher orderbias reduction of the estimators is discussed, and some examples are given.

著者

Akahira Masafumi

出版者

日本統計学会

雑誌

Journal of the Japan Statistical Society (ISSN:03895602)

巻号頁・発行日

vol.19, no.2, pp.179-196, 1989

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The problem on jackknifing estimators is investigated in the presence of nuisanceparameters from the viewpoint of higher order asymptotics. It is shown that theasymptotic deficiency of the jackknife estimator relative to the bias-adjusted maximumlikelihood estimator (MLE) is equal to zero under true and assumed m.odcls. Moreover,the asymptotic deficiency of the MLE or the jackknife estimator under the assumedmodel relative to that under the true model is given.

著者

Akahira Masafumi Sato Michikazu Torigoe Norio

出版者

日本統計学会

雑誌

Journal of the Japan Statistical Society (ISSN:03895602)

巻号頁・発行日

vol.25, no.1, pp.1-18, 1995

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Recently a new approximation to a percentage point of non-centralt-distributions was proposed by Akahira [1]. In this paper the approximationformula is presented and the existence and uniqueness of a solution of theequation on the formula is proved. Numerical results are also given.

著者

Akahira Masafumi

出版者

日本統計学会

雑誌

Journal of the Japan Statistical Society (ISSN:03895602)

巻号頁・発行日

vol.23, no.1, pp.19-31, 1993

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In the presence of a nuisance parameter the asymptotic deficiency of the discretizedlikelihood estimator (DLE) relative to the bias-adjusted maximum likelihood estimatoris obtained under the assumed model. It consists of two parts. One is the lossof information associated with the DLE of the parameter to be estimated. Another,is that due to the "incorrectness" of the assumed model. Some examples on the normaland Weibull type distributions are given.

著者

Akahira Masafumi Takahashi Kunihiko

出版者

日本統計学会

雑誌

Journal of the Japan Statistical Society (ISSN:03895602)

巻号頁・発行日

vol.31, no.2, pp.257-267, 2001-12

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For a sum of independent discrete random variables, its higher order large-deviation approximation is discussed. An approximation to the tail probability of the distribution of the sum is provided, and its numerical comparison with other approximations is done in the binomial case. Consequently, the approximation formula is seen to be more accurate.

著者

Maihara Hirosuke Akahira Masafumi

出版者

日本統計学会

雑誌

Journal of the Japan Statistical Society (ISSN:03895602)

巻号頁・発行日

vol.34, no.2, pp.189-206, 2004-12

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From the decision-theoretic viewpoint, using a weighted loss we compare the risks of testing procedures in the location and scale parameter cases. We also get numerically the minimax solution of Bayes testing procedures w. r. t. a parameter of the prior distribution, under the weighted loss.