A Class of Selection Procedures for Location Parameters Using Sub-sample Medians

Abstract

Let Π₁, … , Π _k be k independent populations and let F _i (x) = F(x −  μ _i ) be the absolutely continuous cumulative distribution function (cdf) associated with the population, Π _i , i = 1, … , k. The problem is to select a subset of k populations containing the one associated with the largest location parameter. A class of subset selection procedures based on sub-sample medians for unequal sample sizes is proposed and compared with the existing procedures in the sense of Pitman asymptotic relative efficiency (ARE), with interesting results. The proposed procedures can approximately be implemented with the help of existing tables. Simulation study is carried out to know the sample size required for the implementation of the proposed class of procedures.

Keywords:

• Subset selection
• Sub-sample medians
• Correct selection
• U-Statistics
• Asymptotic relative efficiency (ARE)

Acknowledgment

We would like to thank the anonymous reviewer for careful reading of the article and many helpful comments.