Selecting the normal population with the smallest variance: A restricted subset selection rule
Document Type
Article
Publication Date
8-18-2017
Abstract
Consider k(⩾ 2) normal populations whose means are all known or unknown and whose variances are unknown. Let σ2[1] ⩽ ⋅⋅⋅ ⩽ σ[k]2 denote the ordered variances. Our goal is to select a non empty subset of the k populations whose size is at most m(1 ⩽ m ⩽ k − 1) so that the population associated with the smallest variance (called the best population) is included in the selected subset with a guaranteed minimum probability P* whenever σ2[2]/σ[1]2 ⩾ δ* > 1, where P* and δ* are specified in advance of the experiment. Based on samples of size n from each of the populations, we propose and investigate a procedure called RBCP. We also derive some asymptotic results for our procedure. Some comparisons with an earlier available procedure are presented in terms of the average subset sizes for selected slippage configurations based on simulations. The results are illustrated by an example.
Publication Title
Communications in Statistics - Theory and Methods
Volume
46
Issue
16
First Page
7887
Last Page
7901
Digital Object Identifier (DOI)
10.1080/03610926.2016.1165849
ISSN
03610926
E-ISSN
1532415X
Citation Information
Buzaianu, Chen, P., & Panchapakesan, S. (2017). Selecting the normal population with the smallest variance: A restricted subset selection rule. Communications in Statistics. Theory and Methods, 46(16), 7887–7901. https://doi.org/10.1080/03610926.2016.1165849