Abstract #300634

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JSM 2003 Abstract #300634
Activity Number: 126
Type: Contributed
Date/Time: Monday, August 4, 2003 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #300634
Title: Estimation of the Minimum Mean of Normal Populations under the Tree Order Restriction
Author(s): Sanjay Chaudhuri*+ and Michael D. Perlman
Companies: University of Washington and University of Washington
Address: Dept. of Statistics, Seattle, WA, 98195-0001,
Keywords: maximum likelihood estimation ; order restriction ; tree order ; consistency
Abstract:

We consider k+1 univariate normal populations with common variance \sigma^2 and means \mu_i, i=0,1,2,.,k, constrained by the tree order restriction \mu_0\le\mu_i, i=1,2,.,k. The maximum likelihood estimator of \mu_0 is known to diverge to -\infty a.s. k-->\infty if all means \mu_i are bounded and all sample sizes \n_i remain finite. However, this is not true if the means are unbounded or more importantly if n_0 increases with k, which is the case of most practical interest. In such cases it can be shown that the m.l.e. of \mu_0 is consistent or can be easily adjusted to attain consistency. The consistency of a modified version of an estimator due to Cohen and Sackrowitz (2002) also will be discussed.

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