Journal of the Japan Statistical Society, Japanese Issue

LEVERAGE POINTS IN NONLINEAR REGRESSION MODELS

Yasuto Yoshizoe

1991 Volume 21 Issue 1 Pages 1-11
Published: 1991
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.21.1

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We give a general definition of the leverage point in the general nonlinear regression model. including the linear regression model, In particular, the definition can be applied to binary regression models, such as the logit and the probit models. This approach makes clear when and why the ordinary definition of leverage points based on the diagonal clement of the hat matrix makes sense.

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TRENDS AND STRUCTURAL CHANGES IN MACROECONOMIC TIME SERIES

Yoshiyuki Takeuchi

1991 Volume 21 Issue 1 Pages 13-25
Published: 1991
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.21.13

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Many empirical studies have dealt with unit roots in the context of examining the trend properties of economic time series. However, these studies have not considered the possibility of structural changes in the trends of the time series data. In this paper, we propose models of trends that incorporate structural change and examine them with unit-root-test procedures. It is concluded that the trend properties of the Japanese GNP switched from having a unit root to no unit root. Using a stepwise Chow-test technique, we find that the point of structural change is not the first oil shock period but the period when a regime change occurred in the exchange rate system.

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PRELIMINARY TEST AND EMPIRICAL BAYES APPROACH TO SHRINKAGE ESTIMATION OF REGRESSION PARAMETERS

Abdunnabi M. Ali, A. K. Ehsanes Saleh

1991 Volume 21 Issue 1 Pages 27-42
Published: 1991
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.21.27

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The problem of estimating the regression coefficients in the usual regression model is considered when it is a priori suspected that the coefficients may be restricted to a subspace. Four estimators, namely, the unrestricted least squares estimator (ULSE), restricted least squares estimator (RLSE), preliminary test estimator (PTE) and shrinkage estimator (SE) are given. Further, we show that proposed SE is the empirical Bayes estimator (EBE) under certain prior distribution. The RLSE has the smallest risk when the hypothesis that the regression coefficients satisfy the restriction holds. However, the risk of RLSE is unbounded when the parameter moves away from the subspace of the restriction. The SE has the smallest risk in most cases except when the parameter is in near the null hypothesis; in such case the PTE is better.

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AN ANALYSIS OF VARIANCE OF PARTIALLY BALANCED FRACTIONAL 2^m1+m2 FACTORIAL DESIGNS OF RESOLUTION V

Masahide Kuwada

1991 Volume 21 Issue 1 Pages 43-59
Published: 1991
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.21.43

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By using the algebraic structurc of the extended triangular multidimensional partially halanced association scheme, this paper gives an analysis of variance of a partially balanced fractional 2^m1+m2 factorial design of resolution V derived from a partially balanced array.

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ON POSITIVE-PART SHRINKAGE R-AND M-ESTIMATION IN ONE-WAY ANOVA

Taka-aki Shiraishi

1991 Volume 21 Issue 1 Pages 61-72
Published: 1991
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.21.61

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In a one-way analysis of variance, positive-part shrinkage versions of the R-estimators for the additive treatment constants are proposed, a long with amodified James-Stein estimation rule, when it is doubtful whether the parameters are null. The asymptotic distributional risks of the R-estimators, the proposed estimators, and the preliminary-test and shrinkage R-versions under an arbitrary quadratic loss are derived, and the relative risks arc studied. Under a special feasible quadratic loss, it is shown that the positive-part shrinkage R-estimators dominate the other estimators. R-estimators for the grand mean and for population means are discussed. The same discussions are presented for versions of the M-estimation.

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THE MOVER-STAYER MODEL AND A PROCEDURE FOR THE MAXIMUM LIKELIHOOD ESTIMATION OF THE PARAMETERS

Nobuoki Eshima

1991 Volume 21 Issue 1 Pages 73-83
Published: 1991
Released on J-STAGE: August 24, 2009

DOIhttps://doi.org/10.11329/jjss1970.21.73

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The mover-stayer model (Blumen, et al. [6]) was proposed for explaining timedependent human behavior. In the originally proposed model, it was assumed that a population is divided into two types of individuals, i.e., “movers” and “stayers”. The mover changes states at any time point according to a time-homogeneous Markov chain, whereas the “stayer” does not change states over time. This model is an attempt to explain time-dependent human bchavior in a heterogencous population. In the present paper, the mover-stayer model is extended to the case where the mover changes states according to a Markov chain with time-dependent transition matrices, and a simple method for obtaining the maximum likeidood estimates of the parameters in the model is constructed. Moreover, the model is applied to real data in the sociometric area to illustrate the estimation procedure.

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THE LAW OF THE ITERATED LOGARITHM FOR THE TWO-SAMPLE EMPIRICAL PROCESS AND CHERNOFF-SAVAGE STATISTICS

In-Sun Chu, Shingo Shirahata

1991 Volume 21 Issue 1 Pages 85-95
Published: 1991
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.21.85

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Pyke and Shorack (1968) proved the weak convergence properties of the two-sample empirical process. In this paper, we prove the law of the iterated logarithm for the two-sample empirical process and Chernoff-Savage statistics with respect to ρ_q-metrics as described in Wellner (1977 b).

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STATISTICAL GRAPHICS: A CLASSIFIED AND SELECTED BIBLIOGRAPHY

Masashi Goto, Yoshihiro Matsubara, Akio Yoden, Yoshihide Tsuchiya, Kaz ...

1991 Volume 21 Issue 1 Pages 97-121
Published: 1991
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.21.97

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This paper presents a bibliography on statistical graphics, consisting of 323 articles (42 in books and 281 papers) published mainly after 1970. For convenience of reference, we attach to each article a symbol expressing its main purposes. For each research field defined by a symbol, we aggregate the number of articles and examine recent research trends. We then show the relationship between graphical and formal methods in the form of a galaxy, in order to clarify the purpose of statistical graphics. It is clear that recent popularity of statistical graphics is supported by developments in computer science and the accompanying equipment of computing environments. Thus, we comment on computing environments for statistical graphics and present annotated references to the literature. We hope this bibliography will provide a guidepost to subsequent researchers in the area of statistical graphics and suggest directions for future development.

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Simultaneous Estimation of Structural Change and Functional Form in Aggregate Export Functions

Kazutoshi Ueyama

1991 Volume 21 Issue 1 Pages 123-129
Published: 1991
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.21.123

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The Measurement of Price Expectations and a Test of the Hypothesis of the Natural Rate of Unemployment in Japan

Zhi Dong Li, Satoru Kanoh

1991 Volume 21 Issue 1 Pages 131-145
Published: 1991
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.21.131

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[in Japanese]

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Book Reviews

[in Japanese], [in Japanese], [in Japanese], [in Japanese], [in Japane ...

1991 Volume 21 Issue 1 Pages 147-153
Published: 1991
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.21.147

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