この論説は,国内国外での研究生活で筆者が体験したことの中から,わが国の統計事情のもとで,今日でも参考になることを期待して話題を選び,平易な形にまとめたものである.
筆者の1986年の論文[10]において,わが国において統計教育研究体制の早急な整備が必要であることを論じた.そこには筆者のいくつかの体験談が含まれており,ここでは重複を避けて話題選択を行ったが,論文[10]をこの論説と合わせて読み返していただければ,筆者の意図していることがよりはっきりすると思う.
話題として取り上げている体験自体は古い時代のものであるが,現在でも,今日的な意味に修正されて鮮明に残っており有益な参考となり得るであろうと希っているのである.

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In this paper, we consider a test statistic for testing the goodness of fit of a completely specified null distribution. The statistic is based on a characterization of the uniform distributions. Since any continuous distributions can be transformed to the uniform distribution over the unit interval, it is consistent for any alternative distributions. The power properties of our test are not so excellent. However, since no test statistics based on characterizations arc known, our test will be worth considered.

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For the covariance matrix of the multivariate normal distribution with an unknown mean vector, discontinuous or continuous Stein type truncated estimators have been proposed. This article summarizes a series of recent results and obtains an improved and generalized Bayes estimator based on the Brown-Brewster-Zidek method, well known in the univariate case. The asymptotic risk expansions of the estimators are derived, numerically investigated, and it is revealed that the risk-reductions of the generalized Bayes estimator and an empirical Bayes estimator are considerably great in the large dimensional case.

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This article discusses four estimation methods for the first component mean vector μ₁ of a q-variate normal distribution when it is suspected that μ₁=μ₂, where μ₂ is the second component mean vector. Exact bias and risks of all of these estimators are derived and their efficiencies relative to a classical estimators are studied. An optimum rule for the preliminary test estimator (PTE) is discussed. The range in the parameter space where preliminary test estimator dominates shrinkage estimator is investigated. It is shown that the Stein-rule estimator (SE) dominates the classical one, whereas none of the PTE and SE dominate each other. The range in the parameter space where PTE dominates SE is also investigated. It is found that SE outperforms the PTE except in a range around the null hypothesis. Further, for large values of α, the level of statistical significance, SE dominates the PTE uniformly. The relative dominance picture of the estimators is presented.

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Exact confidence regions for the binomial parameter p were given by Sterne [9]. However, they are not always interval-valued. In this paper, Steme's confidence intervals are reanalyzed, and modified confidence intervals are presented. Our improved confidence intervals have the minimum total length and have the maximum acceptance probabilities among all confidence intervals with minimum total length. Ancfficient algorithm for the confidence intervals is also presented.

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Asample is taken from a mixture of two subpopulations. The characteristics of the two sub-populations are to be estimated. If each observation in the sample is completely identiFIed, that is, if one knows which observation comes from which sub-population, then the estimation can follow standard methods and it is straightforward. However, if the observations are not identified, then some clustering Procedure has to beapplied to classify the observations into two sub-populatiolls. A reasonable estimate turns out to be an inconsistent estimate as long as there is a chance of misclassification. This note introduces a general method of estimation after clustering. This estimation procedurc subsumes the reasonablc method when the identities of the observations are known.
A concept of fuzzy partition is employed here to by-pass the problem of misclassi-fication. Two examples will be discussed. One example will involve a parametric classification procedure and the other will involve a nonparametric clustering procedure called K-means. A Monte Carlo study will be conducted to compare the estimates arising from a classical clustering procedure and a fuzzy clustering procedure.

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In a linear regression model, some shrinkage type regression predictors are examined in a situation where a prediction area is different from a sample area. This is then evaluated from the perspective of an estimation error of shrinkage parameter to estimate from a sample. The goodness of the shrinkage regression predictor is appraised on the basis of the expectation of Prediction Mean Square Error (PMSE) with respect to the model condition parameter following a prior distribution. A modified shrinkage predictor is proposed.

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Suppose we have the observations of a stochastic process {X_t} and we are required to predict its future values. There are many forecasting methods that might be used. However, it is difficult to decide which method we should adopt, since the accuracy of a forecasting method often depends on the properties of {X_t}, which can not be clearly known in many practical situations. In this paper, we investigate some aspects on robustness of the simple exponential smoothing method (SES). We will consider whether or not the forecasts provided by SES are reasonable not only when {X_t} is stationary but also when {X_t} deviates from a stationary process. For that purpose, we show prediction errors of the SES predictor for a wide class of stochastic processes, and we show comparisons of the prediction errors between this predictor and another predictor which is widely used.

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It has been pointed out that the solutions in a latent class analysis are seriously unstable. There seems to exist two causes of the instability. One is a geometric structure in a latent class model and the other is a property of the methods for solving the latent structure equations. In the latter there are several methods that have been proposed so far. A robust method which copes with the instability of the model, however, has not, yet been proposed. In this paper we will only treat the latent class analysis with two classes. The aim is to suggest a criterion on the choice of a left signature and a stratifier of Gibson's method, so that the method may become a robust one. Moreover in order to get highly reliable solutions we shall give a new proposal to develop items, i.e., questionnaire. A numerical example will be given.

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Type II Tobit models are widely used in various feilds of economics, such as labor economics. These models are also known as models with sample-selection biases. Because of its computational difficulty, the maximum likelihood estimator (MLE) is seldom used to estimate these models, while Heckman's two-step estimator (Heckman [1976 and 1979]) is widely used to estimate these models. However, Heckman's two-step estimotor sometimes performs poorly and the MLE is known to be a better estimator. In this paper, I point out some of the limitation of Heckman's two-step estimator, and I compare the two estimators by the Monte Carlo experiments. I also present the computor program which makes possible to calculate the MLE.

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まず最初に,長野県内の年最大1・2・3日降水量時系列に存在する非定常性を原系列及び1, 2乗の移動部分標本系列の回帰直線の傾きから検証した.次いでそれにグンペル分布を当てはめた場合のその分布のパラメータ,すなわち尺度母数と位置母数に存在する非定常性を,移動部分標本におけるパラメータ時系列の回帰直線の傾きから検証した.その結果,データの時系列及びパラメータの時系列の多くに非定常性を見ることができた.最後に,パラメータ時系列を回帰した直線上(外挿部分も含む)のパラメータの値を読み取り,それらのパラメータから決定されるグンペル分布から時間に依存した超過確率水文量,すなわち非定常確率水文量を算定した.得られた結果は,地点毎にまた対象水文量毎にその時系列特性は異なるが,ここでも上述の結果の当然の帰結として,多くの場合非定常性を認めることができ,計画対象時点毎に確率水文量を提示することができた.

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