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, S. Panchapakesan

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1 Citation (Scopus)

Abstract

Consider k(2) normal populations with unknown means 1,., k, and a common known variance σ2. Let [1] ṡṡṡ [k] denote the ordered i.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 [k-t + 1]-[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 i. 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.

Original languageEnglish (US)
Pages (from-to)2250-2259
Number of pages10
JournalCommunications in Statistics - Theory and Methods
Volume43
Issue number10-12
DOIs
StatePublished - May 15 2014

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Subset Selection
Normal Population
Selection Rules
Requirements
Subset
Indifference Zone
Unknown
Population Size
Denote
Configuration
Experiment

Keywords

  • Restricted subset size
  • Selecting normalmeans
  • Subset selection probability requirement

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

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title = "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",
abstract = "Consider k(2) normal populations with unknown means 1,., k, and a common known variance σ2. Let [1] ṡṡṡ [k] denote the ordered i.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 [k-t + 1]-[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 i. 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.",
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AU - Panchapakesan, S.

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N2 - Consider k(2) normal populations with unknown means 1,., k, and a common known variance σ2. Let [1] ṡṡṡ [k] denote the ordered i.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 [k-t + 1]-[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 i. 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.

AB - Consider k(2) normal populations with unknown means 1,., k, and a common known variance σ2. Let [1] ṡṡṡ [k] denote the ordered i.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 [k-t + 1]-[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 i. 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.

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