A numerical comparison of two growth curve models, one with a random-effects covariance structure, and the other a general covariance structure, was made for a complete data set of 455 individuals with measurements of stature conducted annually from ages 10 to 18 years. The components of the variance-covariance matrix of the estimators of regression coefficients for a random-effects covariance structure were larger than those of a general variance-covariance matrix, ranging from 1.1 to 3.0 for the ratios of the elements of diagonal matrices, and 2.4 for an off-diagonal matrix. The ratios of elements of two off-diagonal matrices were about 2.7 and 4.3 if evaluated by an absolute value of these ratios for all elements with opposite signs. While the absolute difference between components in the two cases are small, the test statistics are almost the same except for the test value of the sex difference. The results obtained from the two models show that both are valid for the interpretation of the data set. For the data used here, the general model seems to fit the annually measured data better than the random-effects model for females 10-18 years old at the time of examination (ATE). The fit between observed and expected values is better in the general model for males 16-18 years old ATE, but it is better in the random-effects model for males 10-15 years of age ATE. The Akaike Information Criterion (AIC) value for a complete data set of 455 individuals as a measure of goodness of fit was 20, 953.76 for the random-effects covariance structure, while for the general covariance structure it was 19, 013.40. The random-effects model permits the use of an incomplete data set for 1264 individuals with four or more measurements, However, the results obtained are almost equal to those of a complete data set.

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Suppose that y is a binary variable which takes the values 1 or 0, and P[y=1] is given as a function of a K-dimensional vector x. Dividing the space of x into two regions A and B, so that P[y=1|x]>1/2 if x∈A and P[y=1|x]<1/2 if x∈B, is important for some fields such as neural network computers.
Nawata [1990a, b] proposed a new estimation method which is based on grouping. This paper shows that Nawata's grouping method can be used for the problem mentioned above. In the estimation, the sample space of the independent variables is divided into N cells so that the size of each cell goes to zero as the number of observations goes to infinity. Each cell is labeled as 1 if more than half of the yt's in the cell are 1, and 0 otherwise. The probit maximum likelihood method is then applied to these newly-defined values.

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The asymptotic distributions of the θ, λ and η function estimates for identifying a mixed ARMA process are presented.

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We consider three voting systems and discuss the limiting probabilities of the consistency and the coincidence of election outcomes as the number of voters tends to infinity. To compute the limiting probability, an orthant probability is required for a nonsingular or singular normal distribution. We describe a general method of computing orthant probabilities based on the ideas developed by Nabeya [8] and present simulation results in order to confirm the numerical values of the limiting probabilities.

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A fixed sample procedure for selecting the better of two negative binomial populations in the framework of indifference zone approach is presented. The difference and ratio of success probabilities are used simultaneously to overcome the dependence of mean and variance of negative binomial populations. The resulting sample sizes required to achieve the specified probability of correct selection are observed to be lower compared to the procedure involving only one distance measure. The normal approximation is derived and compared with the exact procedure with respect to the associated sample sizes.

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This paper considers selection of the best population (with respect to mean vector) from several multivariate normal populations. The problem is solved by a subset selection approach. When covariance matrices are unknown, the Hetero-scedastic Method is employed. The asymptotic approximation to the distribution is given for this method.

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We consider the uniform asymptotic normality of the Wishart distribution based on the K-L information. In this paper, we shall give the upper bound of the K-L information.

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This paper introduces a model that is an extension of Goodman's (1985) diamond model, for the analysis of square contingency tables with the same ordinal row and column classifications. The extended model can be viewed as a model of quasiuniform association applied to the diamond shape formed by rotating the square table forty-five degrees. An example is given.

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Although Japan has been experiencing a great change in consumption patterns that may be significantly caused by a transition in household composition, there is an insufficient amount of statistical information about income and consumption details of the subgroups in the household sector. The purpose of this paper is to estimate aggregated household consumption for the period 1984-1988 using the Family Income and Expenditure Survey (FIES) and other sample surveys, and to assess its quality characteristics as compared to the System of National Accounts (SNA). We also consider distinctive features of the consumption behavior of single-headed households. The main findings are that the FIES is about sixty percent of the SNA at an aggregated level and suffers an expanding information leakage during the period. Single-headed households share about one seventh of the total household consumption and grow faster than other groups. How and why the information leakage is generated in the FIES remains unclear.

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