Two-sample problems of estimating p×p scale matrices are investigated under elliptically contoured distributions. Two loss functions are employed; one is the sum of Stein's loss functions of the one-sample problem of estimating a normal covariance matrix and the other is a quadratic loss function for Σ₂Σ^-1₁, where Σ₁ and Σ₂ are p×p scale matrices of elliptically contoured distributions. It is shown that improvement of the estimators obtained under the normality assumption remains robust under elliptically contoured distributions. A Monte Carlo study is also conducted to evaluate the risk performances of the improved estimators under three elliptically contoured distributions.

View full abstract

Pharmacokinetics is the study of the time course of drug absorption, distribution, metabolization, and excretion in the human body. Actually, because we cannot monitor the kinetics of a drug in the human body directly, we observe the serial drug concentration in blood sampled from an individual who received the drug. In practice, intending to describe this time course in the observed drug concentration, we often use a compartment model. In this paper, we focus on nonlinearity of the compartment model and propose the design criterion, MSE_Q-D_opt, for the purpose of selecting the optimal sampling times of the blood drug concentration data. This criterion minimizes the determinant of the mean squared error for the estimates of the parameters in the compartment model. In several numerical examples, the properties of the MSE_Q-D_opt are evaluated. Furthermore, we assume a situation in which we fit the compartment model to the blood drug concentration data that are sampled at the times selected by the MSE_Q-D_opt and the typical optimal design criterion, D_opt, and evaluate the performance of their criteria for the estimation of the parameters in the compartment model. The MSE_Q-D_opt can select the sampling times flexibly and provide more precise estimates of the parameters, compared with the D_opt.

View full abstract

We describe simultaneous diagnostic methods for assessing the influence of an individual case on the estimates of the two transformation parameters in the double power-normal transformation model proposed by Goto, Inoue and Tsuchiya (1987), which attempts simultaneously to achieve the two assumptions of at least approximate normality of the additive errors and linearity or additivity of structure for the expected value of the response in regression analysis. We also consider a simple analogy of the methods discussed by Hinkley and Wang (1988) and Tsai and Wu (1990). Furthermore, we provide a graphical presentation for assessing the degree to which individual cases influence the estimates of the two transformation parameters. Two examples are used to illustrate the proposed method.

View full abstract

In this paper, we study tests of two hypotheses on the distance between two populations with mixed variables, where some are categorical and the others are continuous. This distance is the extended Mahalanobis squared distance on the location model. Asymptotic probability distributions of the test statistics under the hypotheses are introduced, and the performances of the tests are investigated through simulation methods. As a result of all simulations, we recommend that the two hypotheses tests have to be used together to improve each other's weaknesses.

View full abstract

It is important first to grasp the current environmental conditions of information education in the classroom, and in addition, to grasp the current degree of the knowledge that teachers possess about information education and information ethics education. Questionnaires were collected from 456 schools and 10, 637 teachers. The original data and a summary of the survey on “Information ethics education in Japan” are printed in JSCS memorial DVD. Here, this survey will be introduced.

View full abstract