A MONOTONICITY OF MOMENTS CONCERNED WITH ORDER RESTRICTED STATISTICAL INFERENCE

KENTARO NOMAKUCHI

Department of Mathematics and Information Science, Kochi University, Kochi 780-8520, Japan

(Received December 27, 1999; revised March 29, 2001)

Abstract. In the order restricted statistical inference problem, moments of the distance between a true parameter and the least square estimate are non-decreasing when the true parameter moves along a half line from an initial point in the null space. This follows from “stochastically larger” property of the distance.

Key words and phrases: Order restricted statistical inference, least square estimate, maximum likelihood estimate, monotonicity, moments, stochastically larger.