### Abstract

Consider k(⩾ 2) normal populations whose means are all known or unknown and whose variances are unknown. Let σ^{2} _{[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 σ^{2} _{[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 R_{BCP}. 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.

Original language | English (US) |
---|---|

Pages (from-to) | 7887-7901 |

Number of pages | 15 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 46 |

Issue number | 16 |

DOIs | |

State | Published - Aug 18 2017 |

### Fingerprint

### Keywords

- Average subset sizes comparisons
- restricted subset size
- selecting normal variances

### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

*Communications in Statistics - Theory and Methods*,

*46*(16), 7887-7901. https://doi.org/10.1080/03610926.2016.1165849

**Selecting the normal population with the smallest variance : A restricted subset selection rule.** / Buzaianu, Elena M.; Chen, Pinyuen; Panchapakesan, S.

Research output: Contribution to journal › Article

*Communications in Statistics - Theory and Methods*, vol. 46, no. 16, pp. 7887-7901. https://doi.org/10.1080/03610926.2016.1165849

}

TY - JOUR

T1 - Selecting the normal population with the smallest variance

T2 - A restricted subset selection rule

AU - Buzaianu, Elena M.

AU - Chen, Pinyuen

AU - Panchapakesan, S.

PY - 2017/8/18

Y1 - 2017/8/18

N2 - 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.

AB - 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.

KW - Average subset sizes comparisons

KW - restricted subset size

KW - selecting normal variances

UR - http://www.scopus.com/inward/record.url?scp=85018804940&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85018804940&partnerID=8YFLogxK

U2 - 10.1080/03610926.2016.1165849

DO - 10.1080/03610926.2016.1165849

M3 - Article

VL - 46

SP - 7887

EP - 7901

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 16

ER -