Journal of the Japan Statistical Society, Japanese Issue

SOME PROPERTIES OF THE GENERALIZED LOGISTIC AND LOG-GAMMA DISTRIBUTIONS

Hiroyuki Uesaka

1989 Volume 19 Issue 1 Pages 1-13
Published: 1989
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.19.1

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Several properties of the generalized logistic and log-gamma distributions, such as moments and shapes of the distributions, are examined. The relationship between skewness and kurtosis of these distribution families is graphically shown. The degrees of approximations of the generalized logistic and log-gamma distributions to their respective limiting distributions is examined. Furthermore, approximation of the log-gamma distribution by the generalized logistic family is discussed.

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UNBIASED ESTIMATION OF THE AUTOCORRELATION COEFFICIENTS FOR A STATIONARY GAUSSIAN PROCESS WITH KNOWN MEAN AND VARIANCE USING THE SMOOTH CLIPPING FUNCTION

Minoru Tanaka

1989 Volume 19 Issue 1 Pages 15-22
Published: 1989
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.19.15

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This paper discusses the estimation of autocorrelation coefficients for a stationary Gaussian process with known mean and variance. An unbiased estimator which is an extension of the sample autocorrelation and the simplified estimator is proposed. An analytical expression for its variance is derived, and efficiency of the estimator is studied under two models.

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ASYMPTOTIC DISTRIBUTIONS OF TEST STATISTICS FOR THE CONSTANCY OF REGRESSION COEFFICIENTS UNDER A SEQUENCE OF RANDOM WALK ALTERNATIVES

Seiji Nabeya

1989 Volume 19 Issue 1 Pages 23-33
Published: 1989
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.19.23

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The locally best invariant test was suggested by Nabeya and Tanaka [1] under normality for the constancy of regression coefficients against the alternative hypothesis that one component of the coefficients follows a random walk process, and the asymptotic null distributions of the test statistics were derived by them without assuming normality. The main purpose of the present paper is to derive the asymptotic distributions of the test statistics under a sequence of alternatives.

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ON A CHARACTERIZATION OF AUTOREGRESSIVE MOVING AVERAGE PROCESSES BY THE CANONICAL STRUCTURE BETWEEN PAST AND FUTURE SPACES

Hiroshi Shigeno

1989 Volume 19 Issue 1 Pages 35-47
Published: 1989
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.19.35

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In this paper we present a characterization of autoregressive moving average processes by means of the canonical structure between past and future spaces in the sense that a stationary process is an autoregressive moving average process if and only if the process has a finite number of non-zero canonical correlations. We also show a characterization of autoregressive processes by only using the first canonical correlation.

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SELECTION OF PREDICTORS IN A GENERALIZED LINEAR REGRESSION MODEL

Takakatsu Inoue

1989 Volume 19 Issue 1 Pages 49-66
Published: 1989
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.19.49

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In a generalized linear regression model, we consider a problem of selection of predictors, which includes the selection of estimators' type of regression parameters in addition to the selection of variables (models). This problem is quite important to deal the situation where a prediction area is different from a sample area. Based on the evaluation of goodness of predictor on Prediction Mean Square Error (PMSE), we first modify the predictors by changing the Generalized Least Squared estimator or the Ordinary Least Squared estimator, and give a criterion for the selection of predictors when these modified predictors are used. Second, we evaluate the goodness of the selected predictor by this criterion based on the expected PMSE with respect to the selection of predictors. This evaluation is done from a simulation study.

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A UNIFIED APPROACH TO IMPROPER SOLUTIONS OF THE MAXIMUM LIKELIHOOD ESTIMATES

Shinto Eguchi

1989 Volume 19 Issue 1 Pages 67-82
Published: 1989
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.19.67

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This paper is concerned with parametric estimation in a situation where the parameter space is restricted. The maximum likelihood solution often occurs outside the parameter space, which is termed as the improper solution. We take a unified approach to the problem in terms of using a prior density which vanishes outside the parameter space. The modified estimate is defined by minimization of the posterior density. The solution is guaranteed to exist almost surely in the parameter space. The method extends directly to other methods of estimation, the so-called minimum contrast methods. The influence of the modification in asymptotic content is investigated.

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A CONSERVATIVE USE OF HISTORICAL DATA FOR A TREND TEST IN PROPORTIONS

Takashi Yanagawa, David G. Hoel, Gary T. Brooks

1989 Volume 19 Issue 1 Pages 83-94
Published: 1989
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.19.83

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The exact conditional tests for incorporating historical controls in testing for a trend in proportions, which were developed recently by Hoel and Yanagawa (1986), depend on Beta-binomial parameters which are estimated from historical data. This paper considers the conditional test for logistic response by Hoel and Yanagawa, shows the test is sensitive to this source of variability, and discusses a conservative use of the test.

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OPTIMUM CHEMICAL BALANCE WEIGHING DESIGNS WITH NON-HOMOGENEITY OF THE VARIANCES OF ERRORS

Krystyna Katulska

1989 Volume 19 Issue 1 Pages 95-101
Published: 1989
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.19.95

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The paper deals with the problem of estimating individual weights of objects, using a chemical balance weighing design with non-homogeneity of the variances of errors in the usual linear model. A lower bound for the variance of each of the estimated weights from this chemical balance weighing design is obtained, and a necessary and sufficient condition for this lower bound to be attained in given. Also, some optimum chemical balance weighing designs are found.

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The Transition of Some Concepts used in U. S. Census of Manufactures

Takeshi Suzuki

1989 Volume 19 Issue 1 Pages 103-113
Published: 1989
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.19.103

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The census of manufactures enforced in the U. S. has come through three major transitions in its history since 1810. (1) The conceputual changes in “establishment”; (2) The changes in enumuration coverage; and (3) The conceptual changes in “industry” and changes in the principle of “industrial classification.” In (1), it is examined how the idea of “establishment” has separated from the concept of the “enterprise”; and in (2), how the enumuration coverages has been changed under what sort of view point of census of manufactures; then finally in (3), under what kind of condition, the branches of manufacturing have been classified as “industries” and how the standard of “industrial classification” has changed.

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Book Reviews

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

1989 Volume 19 Issue 1 Pages 115-122
Published: 1989
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.19.115

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