Some Optimization Problems in Statistics and Miscellaneous Problems in Statistical Education

Abstract

This article consists of two parts. In Part I, we briefly summarize some results in three kinds of optimization problems, which have been obtained through our many years' study. More specifically, these are concerned with the problems on maximum likelihood estimation of some parameters, on optimization of correlation with a quadratic constraint, and on optimum stratification. Especially for the stabilities of those optimal solutions, some additional examinations are investigated in this study. In Part II, miscellaneous problems of statistical education in Japan today are pointed out, and some discussion on the direction to be developed is given. We also show some action plans and some proposals.