AISM 54, 621-625

© 2002 ISM

## 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.

**Source**
(TeX , DVI )