Variance Estimation for Tree Order Restricted Models

TL;DR

This paper investigates the asymptotic behavior of the maximum likelihood estimator for the common variance in normal populations with tree order restricted means, highlighting conditions affecting its consistency and normality.

Contribution

It provides a detailed analysis of the asymptotic properties of the variance estimator under tree order restrictions, considering different sample size scenarios.

Findings

MLE of variance may be consistent or inconsistent depending on sample sizes.

The asymptotic normality of the variance estimator varies with the order of sample sizes.

Different cases of sample size arrangements affect the estimator's properties.

Abstract

In this article we discuss estimation of the common variance of several normal populations with tree order restricted means. We discuss the asymptotic properties of the maximum likelihood estimator of the variance as the number of populations tends to infinity. We consider several cases of various orders of the sample sizes and show that the maximum likelihood estimator of the variance may or may not be consistent or be asymptotically normal.