On Algorithm for Restricted Maximum Likelihood Estimation Under Tree Order Constraint

Maximum likelihood estimation under order restrictions on parameters is of interest for various problems in statistical computing. Statisticians often incorporate restrictions by using mostly application-specific algorithms. Sometimes the devised algorithms are too complicated to implement or are inefficient in terms of time required to converge. Since it is of interesting that the estimate of means for 𝑘+۱ normal populations with unknown means μ𝑖;𝑖=۰,۱,…,𝑘 which are subject to tree order restriction, μ۰≤μ𝑖 ; for all 𝑖≥۱. Our aim in this paper is to give an iteration algorithm for obtaining the restricted maximum likelihood estimators under the tree order restriction. Some numerical results are given to illustrate how much improvement is obtained over the UMLE and RMLE estimators

Keywords:

Convex cone , Mean squared error , Order constraint , Restricted maximum likelihood