On Finding the Largest Normal Mean and Estimating the Selected Mean
Abstract
For k > or = 2 independent normal populations with unknown means and a common known variance the problem of selecting the population with the largest mean and simultaneously estimating the mean of the selected population is considered in the decision theoretic approach following Cohen and Sackrowitz (1988). Under several loss functions with two additive components due to selection and due to estimation, Bayes decision rules are derived and studied. Both the case of equal sample sizes and the case of unequal sample sizes are treated. The natural rule, which selects in terms of the largest sample mean and then estimates based on the sample mean of the selected population, is critically examined in all situations considered.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1989
- Accession Number
- ADA211628
Entities
People
- Klaus J. Miescke
- Shanti Gupta
Organizations
- Purdue University