Journal of the Japan Statistical Society, Japanese Issue

On the Strategy for the Research of Statistics

Hirotugu Akaike

1989 Volume 19 Issue 2 Pages 123-128
Published: 1989
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.19.123

JOURNAL FREE ACCESS

Download PDF (375K)
ON SOME R-AND M-ESTIMATORS OF REGRESSION PARAMETERS UNDER UNCERTAIN RESTRICTION

A. K. Md. Ehsanes Saleh, Taka-aki Shiraishi

1989 Volume 19 Issue 2 Pages 129-137
Published: 1989
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.19.129

JOURNAL FREE ACCESS

Show abstractHide abstract

For a univariate linear model Y_n=X_nθ+ε_n, when it is apriori suspected that Hθ=h may hold, we are interested in robust estimates of θ. Four classes of point estimations, namely, the unrestricted R-estimators (URE), restricted R-estimators (RRE), the preliminary test R-estimators (PTRE) and shrinkage R-estimators (SRE) are considered. In the light of asymptotic distributional risks, their relative efficiency results under local alternatives are studied in details. Although the SRE may dominate the URE, neither of the SRE nor PTRE dominate each other. We may conclude that the SRE and PTRE are robust relative to the URE and RRE. Furtheremore four versions of M-estimatiors corresponding to the URE, RRE, PTRE and SRE are proposed and the results similar to the cases of the R-estimators are discussed briefly.

View full abstract

Download PDF (321K)
THE RATE OF CONVERGENCE OF FISHER INFORMATION FOR TYPE II CENSORED SAMPLE

Hideto Takahashi, Nariaki Sugiura

1989 Volume 19 Issue 2 Pages 139-144
Published: 1989
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.19.139

JOURNAL FREE ACCESS

Show abstractHide abstract

The convergence rate of the Fisher information for Type II right censored sample standardized by sample size n as n tends to infinity is shown to be O(n^-1/2+γ) for any positive constant γ less than 1/2 when the censoring rate converges to a constant lying in the interval (0, 1). This is proved by rewriting the Mehrotra, Johnson and Bhattacharyya [5]'s expression of the exact Fisher information in terms of the tail probability of binomial distribution and applying the Okamoto [6]'s inequalities. The multiparameter case is also studied.

View full abstract

Download PDF (242K)
AN IDENTIFICATION PROBLEM FOR MOVING AVERAGE MODELS

Masanobu Taniguchi, Myint Swe, Ruriko Taniguchi

1989 Volume 19 Issue 2 Pages 145-149
Published: 1989
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.19.145

JOURNAL FREE ACCESS

Show abstractHide abstract

Consider the following two types of moving average models; Model (1) X_t=e_t+αe_t-1 and Model (2) X_t=αe_t+e_t-1, where |α|<1 and et; t=0, ±1, …, are i. i. d. (0, σ²) random variables with the third-order cumulant c₃. If c₃≠0, it is known that the Models (1) and (2) are identifiable from {X_t}.
In this paper we propose a linear discriminant function, ξ_n, based on the third-order moments of {X_t}, which has a certain optimal property. Using ξ_n we give a method to discriminate between the Models (1) and (2). Numerical studies are given, and they are found to confirm the theoretical results.

View full abstract

Download PDF (154K)
IMPROVEMENTS OF INTERVAL ESTIMATIONS FOR THE VARIANCE AND THE RATIO OF TWO VARIANCES

Yasushi Nagata

1989 Volume 19 Issue 2 Pages 151-161
Published: 1989
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.19.151

JOURNAL FREE ACCESS

Show abstractHide abstract

Let S₀ and S₁ be random variables distributed independently as σ²χ²(n₀) and σ²χ²(n₁, λ), respectively, where χ²(n₀) denotes the central chi-square distribution with n₀ as degree of freedom(d. f.)and χ²(n₁, λ) denotes the noncentral chi-square distribution with n₁ as d. f. and noncentrality parameter λ. A confidence interval for σ² is usually constructed based only on S₀ and its form is [S₀/c₂, S₀/c₁] with c₁ and c₂ some nonzero constants. A confidence interval based on both S₀ and S₁ as an improvement to this existing procedure is proposed. It is linked with the Stein's estimator for σ² which dominates the best equivariant estimator. The improvement of the interval estimation for the ratio of two variances has also been discussed in this paper.

View full abstract

Download PDF (476K)
RESOLVABLE SEMI-REGULASR GROUP DIVISIBLE DESIGNS

D. K. Ghosh, G. C. Bhimani, Sanpei Kageyama

1989 Volume 19 Issue 2 Pages 163-165
Published: 1989
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.19.163

JOURNAL FREE ACCESS

Show abstractHide abstract

A simple and systematic method of constructing resolvable partially balanced incomplete block designs is discussed. This provides a series of resolvable designs for any values of parameters.

View full abstract

Download PDF (130K)
ON SOME COMPARISONS BETWEEN BAYESIAN AND SAMPLING THEORETIC ESTIMATORS OF A NORMAL MEAN SUBJECT TO AN INEQUALITY CONSTRAINT

Hikaru Hasegawa

1989 Volume 19 Issue 2 Pages 167-177
Published: 1989
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.19.167

JOURNAL FREE ACCESS

Show abstractHide abstract

In this paper, we investigate the efficiency of a Bayesian estimator of a normal mean when it is subject to an inequality constraint. There exist many studies which treat the problem of an inequality constraint by utilizing the sampling theoretic approach. However, the problem has not yet been examined by utilizing the Bayesian approach. The purpose of this paper is to introduce a Bayesian estimator of a normal mean subject to an inequality constraint and derive its sampling theoretic risk function. Also, a comparison of the risk performance of Bayesian and sampling theoretic estimators is carried out.

View full abstract

Download PDF (387K)
BEHAVIOUR OF JACKKNIFE ESTIMATORS IN TERMS OF ASYMPTOTIC DEFICIENCY UNDER TRUE AND ASSUMED MODELS

Dedicated to Professor Yukihiro Kodama on his 60th birthday

Masafumi Akahira

1989 Volume 19 Issue 2 Pages 179-196
Published: 1989
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.19.179

JOURNAL FREE ACCESS

Show abstractHide abstract

The problem on jackknifing estimators is investigated in the presence of nuisance parameters from the viewpoint of higher order asymptotics. It is shown that the asymptotic deficiency of the jackknife estimator relative to the bias-adjusted maximum likelihood estimator (MLE) is equal to zero under true and assumed models. Moreover, the asymptotic deficiency of the MLE or the jackknife estimator under the assumed model relative to that under the true model is given.

View full abstract

Download PDF (509K)
OIL CRISIS AND ENERGY DEMAND IN THE JAPANESE MANUFACTURING: REGIONAL DEMENSION

Komei Sasaki, Yoshihiko Tsukuda, Hiroo Shibata

1989 Volume 19 Issue 2 Pages 197-217
Published: 1989
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.19.197

JOURNAL FREE ACCESS

Show abstractHide abstract

The present study is intended to empirically analyse the demand for energy input for each industrial sector at regional level. It especially focuses on identifying the type and the rate of technological change each industry has experienced, and measuring the strength and its change of substitutional or complementary relation between a pair of two factor inputs. Another concern of this study is to examine which industrial sectors have experienced a significant change in the production structure between two periods before and after the oil crisis in 1973. Additionally this paper evolves the relation between the pseudo-R² and conventional R²s for measuring the goodness-of-fit of a simultaneous equation system.

View full abstract

Download PDF (951K)
Long-Memory Models and Their Statistical Properties

Yoshihiro Yajima, [in Japanese], [in Japanese], [in Japanese], [in Jap ...

1989 Volume 19 Issue 2 Pages 219-246
Published: 1989
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.19.219

JOURNAL FREE ACCESS

Show abstractHide abstract

Much attention has recently been paid to long-memory models to analyze many empirical time series with long-range dependence which occur in various fields such as economics and geophysics. This paper gives a survey on their statistical properties and some unsolved problems are also listed.

View full abstract

Download PDF (1334K)
Book Reviews

[in Japanese], [in Japanese], [in Japanese], [in Japanese]

1989 Volume 19 Issue 2 Pages 247-251
Published: 1989
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.19.247

JOURNAL FREE ACCESS

Download PDF (357K)

Register with J-STAGE for free!