"Estimation in Restricted Parameter Spaces" (in Japanese)

In estimation of parameters in restricted spaces, several interesting and surprising results have been developed from a decision-theoretic point of view. For instance, in estimation of a normal mean with a known variance, the sample mean is minimax in the case that the mean is bounded from one side, but it is not minimax in the case of the mean bounded from both sides. Nevertheless, the sample mean becomes minimax even in the case of the mean bounded from both sides if the variance of the normal distribution is unknown. This surprising example inspires us to study more about estimation of the restricted parameter. In this paper, we review several topics in estimation of restricted parameters and explain the interesting results and phenomena derived in the literature from a decision-theoretic aspect.