### Abstract

Consider k(2) normal populations with unknown means _{1},., _{k}, and a common known variance σ^{2}. 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 RH_{p}for 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 RH_{p} 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 (R_{S}) 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 language | English (US) |
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Pages (from-to) | 2250-2259 |

Number of pages | 10 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 43 |

Issue number | 10-12 |

DOIs | |

State | Published - May 15 2014 |

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### Keywords

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

### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

*Communications in Statistics - Theory and Methods*,

*43*(10-12), 2250-2259. https://doi.org/10.1080/03610926.2013.827717

**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.** / Chen, Pinyuen; Hsu, Lifang; Panchapakesan, S.

Research output: Contribution to journal › Article

*Communications in Statistics - Theory and Methods*, vol. 43, no. 10-12, pp. 2250-2259. https://doi.org/10.1080/03610926.2013.827717

}

TY - JOUR

T1 - 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

AU - Chen, Pinyuen

AU - Hsu, Lifang

AU - Panchapakesan, S.

PY - 2014/5/15

Y1 - 2014/5/15

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.

KW - Restricted subset size

KW - Selecting normalmeans

KW - Subset selection probability requirement

UR - http://www.scopus.com/inward/record.url?scp=84902522239&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84902522239&partnerID=8YFLogxK

U2 - 10.1080/03610926.2013.827717

DO - 10.1080/03610926.2013.827717

M3 - Article

VL - 43

SP - 2250

EP - 2259

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 10-12

ER -