From a model selection viewpoint, we propose a new approach to the estimation of two-phase weighted regression functions, setting those models that the change-over points of two-phase regression curves are contained in some divided intervals. The asymptotic distribution of the minimum AIC estimator with respect to the selected model is obtained, when the regression curves in these models are two-phase lines. Further, we apply these two-phase regression models to the analysis of public sensitivities to their environments on the basis of a sample survey data. In this process, we compare the goodness of the selected two-phase regression model with the goodnesses of other regression models, examining if there exists a change-over point.
A minimization problem in metric multidimensional scaling is discussed. Each object is embeded as a point in t-dimensional Euclidean space such that the points minimize the sum of Euclidean norm between the mean of dissimilarity value and Euclidean distance of two points. The existence of a solution which attains the minimum value of the least squares criterion is shown.
For the selection of information in 2-state 2-action statistical decision problem, we proposed a measure of the value of information based on Bayes risk. As an application of this measure, a medical decision problem on the malignancy of bladder tumor is considered and the selection of six information such as stromal pattern, mode of pedunculation, size and number of tumors, cell differentiation and tumor invasion is discussed from both statistical and medical points of view. Independence of information is assumed as the first approximation to the real problem.
Four criteria are proposed for variable selection in factor analysis. Three are introduced from the viewpoint to make the configurations of the true factor scores F and the estimated factor scores F(m) as close as possible. The remaining one comes from the maximization of the variance-covariance matrix due to regression of F on the variables X(m). The relationship among the four criteria and the generalized coefficient of determination (GCD) proposed by Yanai (1980) is discussed. The performances are investigated through the analyses of two sets of real data. As variable selection procedures we propose the forward selection procedure as well as the backward elimination procedure.
This paper presents a simplified approach to Bayesian multivariate analysis of variance (MANOVA) using a cell mean parametrization with specific application to growth curve analysis. With the proposed approach for MANOVA, all cell mean vectors and multivariate treatment contrasts are estimable regardless of the nature of the design when appropriate prior distributions are specified. With the usual multivariate normal model, the distributions of linear contrasts of vector cell means are shown to be obtainable from a matric-variate t distribution. Polynomial effects of time are also considered in order to provide a model for the analysis of longitudinal data.
A bivariate distribution of which one variate has a normal distribution and another variate has a lognormal distribution is considered. It is called semi-lognormal distribution in the present paper. Among several estimation methods, the method of moment is mainly examined. When sample moments are only available and raw data are lost, we have no choice except using the method of moment. The efficiency of the estimator must be considered for practical research works. Then we give asymptotic variances of the estimators and compare them with maximum likelihood estimators, which are asymptotically effecient. Some figures of asymptotic relative efficiencies of the estimators given by the method of moments are also shown.