A Restricted Subset Selection Rule for Selecting at Least One of the t Best Normal Populations in Terms of Their Means When Their Common Variance is Known, Case II
Pinyuen Chen, Lifang Hsu, Shanker Shyam S. Panchapakesan · Communication in Statistics- Theory and Methods · 2014
Consider k( ⩾ 2) normal populations with unknown means μ1, …, μk, and a common known variance σ2. Let μ[1] ⩽ ⋅⋅⋅ ⩽ μ[k] denote the ordered μi.The populations associated with the t(1 ⩽ t ⩽ k − 1) largest means are called the t best populations. Hsu and Panchapakesan (2004) proposed and investigated a procedure RHPfor selecting a non empty subset of the k populations whose size is at most m(1 ⩽ m ⩽ k − t) so that at least one of the t best populations is included in the selected subset with a minimum guaranteed probability P* whenever μ[k − t + 1] − μ[k − t] ⩾ δ*, where P* and δ* are specified in advance of the experiment. This probability requirement is known as the indifference-zone probability requirement. In the present article, we investigate the same procedure RHP for the same goal as before but when k − t < m ⩽ k − 1 so that at least one of the t best populations is included in the selected subset with a minimum guaranteed probability P* whatever be the configuration of the unknown μi. The probability requirement in this latter case is termed the subset selection probability requirement. Santner (1976) proposed and investigated a different procedure (RS) based on samples of size n from each of the populations, considering both cases, 1 ⩽ m ⩽ k − t and k − t < m ⩽ k. The special case of t = 1 was earlier studied by Gupta and Santner (1973) and Hsu and Panchapakesan (2002) for their respective procedures.