J. Japan Statist. Soc., Vol. 31 (No. 1), pp. 111-127, 2001
Abstract. This paper is concerned with an inequality for MSE in statistical prediction theory. Takeuchi (1975) provided the inequality for a risk of unbiased predictor under certain regularity conditions. We shall provide an inequality for MSE of an unbiased predictor from L2-differentiability of densities point of view. In addition, this inequality is simplified and corresponded to the above under slightly stronger conditions. We shall also state the criterion for L2-differentiability in the case that an observable random vector and a predictive random variable are not independent.
Key words and phrases: unbiased predictor, Cramér-Rao inequality, differentiability in quadratic mean.