Journal of the Japan Statistical Society, Japanese Issue

History in Quantitatiove Aspects

Sake Brewing Industry in the Meiji Era

Takafusa Nakamura

1987 Volume 17 Issue 2 Pages 101-105
Published: 1987
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.17.101

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A NOTE ON OUTLIER-PRONE AND OUTLIER-RESISTANT DISTRIBUTIONS

Rinya Takahashi

1987 Volume 17 Issue 2 Pages 107-112
Published: 1987
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.17.107

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Neyman and Scott [6] have considered the ideas of outlier-proneness and outlier-resistance of families of distributions, on the other hand Green [4] has considered the ideas of outlier-proneness and outlier-resistance of individual distributions. In this note, it is shown that the family of Weibull distributions is outlier-prone completely, and some properties of outlier-proneness and outlier-resistance of distributions are shown.

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OPTIMAL DESIGNS MINIMIZING MEAN SQUARED ERROR FOR POLYNOMIAL REGRESSION

Ryuei Nishii

1987 Volume 17 Issue 2 Pages 113-118
Published: 1987
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.17.113

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The paper considers the optimal design which minimizes the integrated mean squared error for polynomial regression when the model may not be correctly specified. We obtain a necessary condition to be optimal and derive several optimal designs.

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SMALL SAMPLE PROPERTIES OF THE TWO-STAGE AITKEN PREDICTOR UNDER SPECIFICATION ERROR

Kazuhiro Ohtani, Sumio Kakimoto

1987 Volume 17 Issue 2 Pages 119-128
Published: 1987
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.17.119

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In this paper, we examine the small sample properties of the two-stage Aitken estimator under the specification error (omitted variables). It is shown analytically and numerically that the predictor incorporating the two-stage Aitken estimator becomes less efficient than the predictor incorporating the ordinary least squares estimator as the magnitude of the specification error gets larger, even if heteroscedasticity is severe. In addition, an empirical example is given in the final section.

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AN ITERATED VERSION OF THE GAUSS-MARKOV THEOREM IN GENERALIZED LEAST SQUARES ESTIMATION

Yasuyuki Toyooka

1987 Volume 17 Issue 2 Pages 129-136
Published: 1987
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.17.129

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In the general linear model with covariance structure, depending on an unknown parameter vector, it is shown that the greatest lower bound for the risk matrix of the generalized least squares estimator (GLSE) constructed with covariance structure estimated from the iterated residuals is that of the Gauss-Markov estimator. A sufficient condition for the existence and the unbiasedness of the GLSE based on iterated residuals is given. It is shown that the use of the iterated residuals does not improve the risk matrix of GLSE through terms of order n^-2 relative to that of the two step estimator.

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ESTIMATION OF THE AUTOCORRELATION COEFFICIENTS IN A STATIONARY LOGNORMAL PROCESS

Minoru Tanaka

1987 Volume 17 Issue 2 Pages 137-148
Published: 1987
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.17.137

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The sequence of positive random variables {Y_t} is called a stationary lognormal process with parameters μ, σ² and ρ_h, h=0, ±1, ±2, …, if the sequence of logarithmic variables {ln Y_t} is stationary and Gaussian with mean μ, variance σ² and autocorrelation coefficients ρ_h. This paper deals with the problem of estimating the autocorrelation coefficients of a stationary lognormal process with known μ and σ². Efficiency of the usual sample autocorrelations relative to a simplified estimate is studied under the assumption that the transformed process is Markovian. The result leads to the choice of the biased simplified estimate as a better estimate than the unbiased sample autocorrelations for small lag h and small σ. Other unbiased estimates are constructed and their variances are evaluated.

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DOUBLE POWER-NORMAL TRANSFORMATION AND ITS PERFORMANCES

AN EXTENSIVE VERSION OF BOX-COX TRANSFORMATION

Masashi Goto, Toshiaki Inoue, Yoshihide Tsuchiya

1987 Volume 17 Issue 2 Pages 149-163
Published: 1987
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.17.149

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In this paper, we propose double power-normal transormation that can effectively be used in the analysis of linear models and also in regression analysis, where achievement of the normality of transformed response variable and the linearity of its expected value as a predictor are treated separately. We examine the effectiveness of our transformation with some examples. To investigate the performances of our double powernormal transformation (DPNT), we compare it with the ordinary power-normal transformation (PNT) by Box and Cox (1964), and also with the marginal and joint powernormal transformations for explanatory and response variables proposed by Goto et al. (1983). From these results, we recommend the DPNT as a complementary transformation of the PNT, in the view of covering a certain kind of extended situation different from those seen for the PNT.

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ROBUSTNESS OF t-TEST

Takeaki Kariya, B. K. Sinha, N. C. Giri

1987 Volume 17 Issue 2 Pages 165-173
Published: 1987
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.17.165

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In this paper we establish the optimality robustness of Student's t-test mainly without invariance. This generalizes some well-known results of Lehmann and Stein (1949), and Kariya and Eaton (1977).

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UNBIASED VARIABLE SELECTION PROCEDURE IN REGRESSION MODELS

Yasushi Nagata

1987 Volume 17 Issue 2 Pages 175-183
Published: 1987
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.17.175

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The unbiasedness of the variable selection procedure in linear regression models is considered. Sawa and Takeuchi (1977) treated two model case, which is extended to three model case in this paper. Two kinds of definitions for the unbiased variable selection procedures are given: for the weakly unbiased one and for the strongly unbiased one. The weakly unbiased procedure based on Mallows' C_p statistic is obtained, and is compared with the original C_p statistic.

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SELECTION OF PREDICTORS AND VARIABLES OF THE LINEAR REGRESSION MODEL WITH AUTOCORRELATED ERROR TERM

Takakatsu Inoue

1987 Volume 17 Issue 2 Pages 185-192
Published: 1987
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.17.185

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Goldberger [1] derived a Best Linear Unbiased Predictor in a case of correlated error. For the case when the model is not necessary true, we first evaluate the goodness of the predictor of Goldberger in the expectation of Prediction Mean Square Error with respect to future sample point, and compare it with the ordinary predictor. We modify the predictors by changing the Generalized Least Squares estimator of regression parameters. We also propose a criterion for selection of predictors and variables when these two modified predictors are used.

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Summary of Reports Presented at the 55th Annual Meeting of the Japan Statistical Society, July 1987

1987 Volume 17 Issue 2 Pages 193-207
Published: 1987
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.17.193

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