Methods of construction of group divisible designs are discussed in this paper. Making use of these methods, a new group divisible design and nine new non-isomorphic solutions for group divisible designs are given in the same range of parameters as in Clatworthy (1973).

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In this paper, attention is focused on the analysis of variance and hypothesis testing of balanced fractional r^m×sⁿfactorial designs of resolution V. These designs are derived from asymmetrical balanced arrays of strength 4 using the algebraic structure of the multidimensional relationship.

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An ANOVA model for estimating three-factor interaction effects in a three-way layout without replication is presented. The model is an application of Tucker's three-mode principal component model to residuals obtained by the elimination of main effects, two-factor interaction effects, and of the general mean. The idea of an interaction element between two levels of a factor is extended to the three-factor interaction effect. It is shown that the co-ordinates of the levels of the factor obtained by applying the principal co-ordinate analysis to the association matrix formed from the three-factor interaction elements correspond to the estimates of the multiplicative terms which represents a three-factor interaction in the ANOVA model. The relationship makes it clear how the multiplicative terms in the model should be interpreted. An numerical example is illustrated.

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This paper presents lower bounds for the minimax risk under quadratic loss, derived from information inequalities for the Bayes risk obtained by Borovkov and Sakhanienko, Brown and Gajek. In addition, admissibility of a minimax estimator is discussed, and we provide examples which illustrate that they are good bounds.

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Normal approximation to the distribution of the estimated process capability index _??__pk is discussed. The direct normal approximation to _??__pk and an alternative approach are compared in terms of skewness and kurtosis. It is shown that the latter approach improves on the former one.

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In this paper we will study the asymptotic behavior of tail probability of the sequential maximum likelihood estimator for the exponential class. This class contains many important stochastic processes including the Wiener process, Bernoulli process, Poisson process, gamma process, and Gaussian autoregressive process, etc. We introduce a stopping time which is useful in sequential statistical analysis. It is shown that the tail probability of the sequential maximum likelihood estimator based on the stopping time decreases exponentially fast as the stopping boundary diverges, and some examples are verified.

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Besides the well-known linear or circular trait, the spherical trait is introduced in correspondence analysis of artificial data. Five types of regular polyhedrons are used as the item pattern. The trait always has three dimensions. Furthermore, solid spherical data can be constructed by adding the center and, if necessary, one or more concentric polyhedrons. Then the data set also has a linear trait representing the radius, which may compete with the spherical trait, hindering a few of the largest eigenvalues in reproducing the item pattern faithfully.

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This paper considers two estimation methods for count data with a power variance function. One is the maximum likelihood method based on a negative binomial model with a power variance function which is not the standard application of a negative-binomial model. Another is the quasilikelihood/pseudolikelihood (QL/PL) estimating equation method. The QL/PL method is a robust method and is applicable to a more general exponential dispersion model with a power variance function. The asymptotic efficiency of the QL/PL estimates were calculated relative to the maximum likelihood estimates, and demonstrated that the mean parameter estimate is approximately fully efficient. If the power parameter of the variance is close to one, then the efficiency of the power parameter of the variance is close to one. It was also found that, in a negative-binomial model with power variance function, mean parameter estimates and variance parameter estimates are approximately asymptotically independnet. An example of data analysis using power variance function is given.

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There are two kinds of experiments e₀ and e₁, and by performing e₀ or e₁, an observation is obtained from the exponential distribution with a parameter 1 or u, respectively. Although the true value of u is unknown, u has a gamma distribution as the prior distribution. The action a_i (i=0, 1) is defined to select e_i, and perform it simultaneously m times. An n-stage sequential decision problem, in which a₀ or a₁ is selected at each stage by considering the information obtained up to that stage in order to maximize the expected sum of mn observations, is constructed and formulated by dynamic programming and the optimal strategy is obtained.
The results of this paper illustrate how to calculate the critical value which has an important role in the optimal strategy numerically. The results also gives the optimal strategy for the integer-valued parameter case of the gamma two-armed bandit problem with one arm known.

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