日本統計学会誌

LIMITING MOMENT GENERATING FUNCTION OF CRAMÉR-VON MISES-SMIRNOV GOODNESS OF FIT STATISTICS UNDER NULL LOCAL ALTERNATIVES

Seiji Nabeya

1992 年 22 巻 2 号 p. 113-122
発行日: 1992年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.22.113

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In this paper the limiting distribution of Carmér-von Mises-Smirnov goodness of fit test statistic discussed when the parameters are estimated from the samle. Using the general theory of Durbin (1973 a and b) a method of deriving the limiting moment generating function for the test statistic is proposed under null and under a sequence of local alternatives. Applying this method, the limiting moment generating functions are evaluated for logistic and Cauchy distributions in the case of efficient estimation. Some results of numerical computation are also given.

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THE MULTIVARIATE STUDENTIZED RANGE AND ITS UPPER PERCENTILES

Takashi Seo, Minoru Siotani

1992 年 22 巻 2 号 p. 123-137
発行日: 1992年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.22.123

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The multivariate Studentized range R_max is defined as the positive square root of the maximum of generalized Studentized distances between any two points in a random sample drawn from a multivariate distribution. A short note on the background of R_max is given. Then, for obtaining good approximation to the exact upper percentiles of R_max the modified second approximation method is explained. Under the assumption of normality, the asymptotic expansion formulas necesary to evaluate those percentiles are drived for the large number of drgrees of freedom of the sample covariance matrix. The accuracy of the estimated percentiles is investigated extensively based on Monte Carlo studies. In the studies the simulated distributions of R_max are calculated for selected values of parameters, some of which are presented in this paper. The results obtained by numerical examinations are summarized, in which the valid ranges of parameters for the formulas of the modified second approximation are discussed. Finally, simultaneous pairwise comparesions of mean vectors of m mulitinormal populations are discussed as an example of the use of R_max.

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ASYMPTOTIC EXPANSION FOR STATISTICS RELATED TO SMALL DIFFUSIONS

Nakahiro Yoshida

1992 年 22 巻 2 号 p. 139-159
発行日: 1992年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.22.139

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Using Malliavin calculus we derived asymptotic expansions of mean values of statistics related to small diffusions. Applications to statistics and economics are discussed.

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SMALL SAMPLE PROPERTIES OF GENERALIZED METHOD OF MOMENTS ESTIMATOR WITH MA (1) ERROR

Shigeyuki Hamori, Shin-ichi Kitasaka

1992 年 22 巻 2 号 p. 161-172
発行日: 1992年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.22.161

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This paper analyzes the small sample properties of GMM estimator under the condition that errors are serially correlated. Some of the interesting results are as follows: 1) The standard deviation of parameter estimates tends to decrease as the number of lags used for instruments increases. 2) Tauchen (1986) insisted that there is a variance/bias trade-off regarding the number of lags used for instruments. However, we found that this result does not generally hold true. It depends on the law of motion of exogenous variables. 3) The test of overidentifying restrictions is biased toward accepting the specification of the model. The magnitude of this bias increases as the number of lags used for forming instruments increases. The overidentifying restriction test is not affected by the difference of the law of motion. Thus, it can be said that, since the desirable choice of instruments depends on the specification of exogenous variables, it is generally recommended to check the law of motion of the exogenous variables in advance in applied works.

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OPTIMALITY ROBUSTNESS OF CLASSIFICATION INTO ONE OF TWO MULTIVARIATE POPULATIONS WITH UNKNOWN LOCATIONS AND EQUAL SCALE MATRICES

Takahiko Hara

1992 年 22 巻 2 号 p. 173-181
発行日: 1992年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.22.173

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This paper is concerned with a multiple decision problem having location slippage hypotheses in a multivariate regression model. The underlying distribution is assumed to be any member of a class of elliptically contoured distributions. We propose a decision rule based on a generalized version of the sample Mahalanobis squared distance, and show that the decision rule is admissible and minimax for the multiple decision problem. Our multiple decision problem includes the problem of classifying a future observation into one of two multivariate elliptically contoured populations with unknown locations and unknown but equal scale matrices. This is an extension of Kudô (1959) and Das Gupta (1965) where the underlying distribution was normal. Our results indicate that their classification rule is robust in the sense that the optimal properties of their classification rule are carried over to non-normal distributions. Kariya and Sinha (1985, 1989) call this optimality robustness.

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PARSIMONIOUS UNIFORM-DISTANCE ASSOCIATION MODELS FOR THE OCCUPATIONAL MOBILITY DATA

H. Bayo Lawal

1992 年 22 巻 2 号 p. 183-192
発行日: 1992年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.22.183

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This paper examines parsimonious models for both the British and Danish Social Occupational Mobility data. The models examined vary from the uniform association model (Goodman, 1981) to the variable distance models (Haberman, 1974). Both the Akaike (AIC) and the Bayesian (BIC) information criteria are employed for model selection. For the British data, the parsimonious UV (uniform-variable distance) association model is preferred, while for the Danish data, the UF (Uniform-fixed distance) association model is considered to be a good fit and it is also thus preferred. We also study the local odds pertaining to adjacent categories for the chosen models. Our models are preferable (based on the BIC criterion) to the parsimonious QU models introduced by Tomizawa (1990a, b).

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A NOTE ON ESTIMATING BIVARIATE STRUCTURAL RELATIONSHIPS WITH UNPAIRED AND UNEQUALLY REPLICATED OBSERVATIONS

Yoshiko Isogawa

1992 年 22 巻 2 号 p. 193-200
発行日: 1992年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.22.193

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To investigate bivariate linear structural relationships from unpaired and unequally replicated observations, we consider five models with certain types of the error variances. We discuss the maximum likelihood estimation of the parameters for each model and give the asymptotic variance-covariance matrices of the estimators when the number of replication tends to infinity and that of incidental parameters remain fixed.

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ASYMPTOTIC DISTRIBUTIONS OF A TEST STATISTIC IN MULTIVARIATE LINEAR RELATIONSHIPS

Yoshiko Isogawa

1992 年 22 巻 2 号 p. 201-209
発行日: 1992年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.22.201

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For testing problems of the coefficient vectors of p-variate linear functional and structural relationships, the statistic which is based on the multiple correlation coefficient between the null variate and the uncorrelated (p-1) variates is considered. The asymptotic distributions of the test statistic under null hypothesis, where the estimators are substituted for other unknown parameters, are obtained for the functional and the structural relationship respectively. The testing procedures considered in this article are shown to be the same either for the functional or the structural relationship. The computations are illustrated with an example.

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レントをベースとした居住環境の指標化

加藤尚史

1992 年 22 巻 2 号 p. 211-228
発行日: 1992年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.22.211

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When a household chooses a residential land, it takes account of its neighborhood setting. Since the rent of a land is supposed to be a function of its environmental attributes as well as its site characteristics, the valuation of the environmental attributes of a household can be derived from the relation.
This paper explores some possibilities for imputing an index of the environment among districts in an urban area by using rent data. The values of environmental attributes are estimated, multiplied by the corresponding attributes and summed to obtain a score for each district.
Various methods are proposed to construct an all-inclusive index of the environment. The choice of weights and units is crucial to synthesize individual indices. This method seems superior to those in the sense that the index is derived from households' own preferences and expressed in terms of money.

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数量化法第3類の諸問題

丘本正

1992 年 22 巻 2 号 p. 229-239
発行日: 1992年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.22.229

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数量化法第3類についてはこれまでに多くの研究者によって多数の研究がなされているが,個別的な応用の場面に入る前に,一般論としてまだ十分解明されていないテーマがいくつか残されている.もっとも重要な問題の1つは,この方法を適用しようとするときに,情報量としては等価な2つの型,自由選択型と項目カテゴリー型のどちらを選ぶべきかという規準を見つけることである.この研究では,この問題に対する1つの回答を与え,第3類に関する他のいくつかの問題を検討し,また理論的な結果を一二のべる.

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書評

市野省三, 伴金美, 椿美智子, 岩崎学

1992 年 22 巻 2 号 p. 241-247
発行日: 1992年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.22.241

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訂正

1992 年 22 巻 2 号 p. 254
発行日: 1992年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.22.2_254

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