This paper presents a theoretical study on prediction limits constructed for an exponential distribution. It is shown that prediction limits have an optimal property. Some characteristic of prediction limits are also investigated when the true distribution is an increasing failure rate distribution.

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This paper proposes test statistics for goodness-of-fit of the multinomial distribution based on the J-divergence. It derives the asymptotic distribution of the statistics under a simple null hypothesis H^s₀ and its local alternatives H^s_{1, n}. It also derives the asymptotic distribution of the statistics under a composite null hypothesis H^c₀ and its local alternatives H^c_{1, n}.

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In the presence of a nuisance parameter the asymptotic deficiency of the discretized likelihood estimator (DLE) relative to the bias-adjusted maximum likelihood estimator is obtained under the assumed model. It consists of two parts. One is the loss of information associated with the DLE of the parameter to be estimated. Another, is that due to the “incorrectness” of the assumed model. Some examples on the normal and Weibull type distributions are given.

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Multiresponse experiments in two-way layouts with interaction, having equal number of observations per cell, are considered. Statistical procedures of the test, estimation and confidence region, based on M-statistics, for interactions and main effects in the models are proposed. Large sample properties of their procedures as the cell size tends to infinity are investigated. The usual assumption of M-procedures that the underlying distribution is diagonally symmetric is not needed. For the univariate case, it is found that the asymptotic relative efficiencies (ARE's) of the proposed procedures relative to classical procedures agree with the classical ARE-results of Huber's one sample M-estimator relative to the sample mean. By simulation studies, the goodness of the x²-approximate for the significance points of the M-tests is investigated, and it can be seen that the M-estimators are robust with respect to the contaminated distribution. Furthermore M-procedures for two-way MANOVA without interaction are discussed briefly.

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Discrete mixtures of geometric random variables X₁ and X₂ are characterized in terms of (i) relations between the best predictor of max (X₁, X₂) given min (X₁, X₂) and the failure rate of the distribution, and (ii) relations between conditional expectation of some appropriate functions of order statistics on some others and the failure rate of the distributions. The characterizing relations were motivated by the work of Kirmani and Alam (1980) and Dallas (1987).

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The testing problems of the coefficient vectors of multivariate linear relationships are considered, when there are replications, where all the variables involved are subject to errors or fluctuations. A test statistic based on the generalization of Williams't test is derived, and its asymptotic distributions under null hypotheses are obtained for a functional and a structural relationship respectively. The testing procedures are shown to be the same either for a functional or a structural relationship.

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The identifiability of a countable mixture of Weibull distributions and that of a countable mixture of log-normal distributions are studied provided that the supports of mixing distributions are well-ordered sets for a total ordering of the parameter space. Both classes of all finite mixtures of Weibull distributions and all finite mixtures of lognormal distributions are shown to be identifiable as special cases.

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This paper is concerned with the analysis of parallel growth curves of several groups. The covariance structure based on a random-effects model is assumed, which can be introduced to repeated measures naturally and reasonably. The MLE's and the LR tests for two hypotheses are obtained under the random-effects covariance structure. Asymptotic null distributions of these tests are also derived.

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As a part of research on historical statistics, we have reliable data on National Accounts Statistics since the late of 19th century. The LTES project of Hitotsubashi University estimated the data from 1885 to 1940. The Economic Planning Agency published the post-1955 data based on the system advised by UNSO. While the national income estimates were published for the period from 1941 to 1954 by the Economic Planning Agency in the late 1950s, the figures must be examined carefully because the basic data were less reliable owing to the confounded situation of Japan in the wartime and just after the end of war.
This paper tries to obtain relatively reliable level of nominal and real GDP on this period. While the nominal GDP was estinated by the Government of Japan, the statistical discrepancy was very large between the estimates from the production, the expenditure and the distribution side. Judging from the conditions of basic data, we selected the figures from the distribution side for the wartime period (1940-44) and linked them to LTES estimates, The post-1941 nominal income were obtained from the expenditure side estimates with some adjustments on the private consumption. This was linked to post-1955 data mentioned before.
The real GDP are calculated from the quantitative data of production. Since the original data for agriculture and industry did not cover the transaction of underground market, they would have some downward biases and we tried to adjust this biases as far as possible. The production of tertial industry is estimated by two different ways. The quantitative figures are used for the transportation, the construction and the public services. The nominal data in the National Income Statistics are deflated for other sectors. The final results are shown in Table 14.

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