Variance estimation for tree-order restricted models

Abstract

In this article, we discuss the estimation of the common variance of several normal populations with tree-order restricted means. We discuss the asymptotic properties of the maximum-likelihood estimator (MLE) 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 MLE of the variance may or may not be consistent or be asymptotically normal.

Keywords:

• order-restricted inference
• tree-order restriction
• maximum-likelihood estimation
• variance estimation

Acknowledgements

The first author thanks the Department of Statistics and Applied Probability of National University of Singapore, for their kind hospitality. This work was partially supported by the grant number R155000111112 from National University of Singapore.