### Abstract

The coverage probability of an approximate confidence interval on the among-group variance component, σ_{α} ^{2}, in a one-way random model is modeled using generalized linear models techniques. The purpose of the proposed modeling is to derive an empirical relationship between the coverage probability on one hand, and k, n., φ, and the model's variance components on the other hand, where k is the number of groups, n is the total number of observations, and φ is a measure of imbalance for the design used. The latter quantities serve as control variables in the derived model, and the coverage probability is treated as the response variable. Contour plots generated from this model can be easily used to depict the effects of the control variables on the coverage probability. In particular, the plots are utilized to compare four methods for constructing approximate confidence intervals on σ_{α} ^{2}. Additional advantages of the derived model include prediction of the coverage probability for a given method using only specified values of the control variables, and the determination of operating conditions that result in improved coverage probability within the region of interest.

Original language | English |
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Pages (from-to) | 275-294 |

Number of pages | 20 |

Journal | Computational Statistics |

Volume | 20 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2005 Dec 1 |

### Fingerprint

### Keywords

- Contour plots
- Generalized linear models
- Logarithmic link function
- Measure of imbalance
- Response surface methodology
- Unbalanced design

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Computational Mathematics

### Cite this

*Computational Statistics*,

*20*(2), 275-294. https://doi.org/10.1007/BF02789704

**Modeling the coverage probability of a confidence interval on the among-group variance component in the unbalanced random one-way model.** / Lee, Juneyoung; Khuri, André I.; Kim, Kee Whan.

Research output: Contribution to journal › Article

*Computational Statistics*, vol. 20, no. 2, pp. 275-294. https://doi.org/10.1007/BF02789704

}

TY - JOUR

T1 - Modeling the coverage probability of a confidence interval on the among-group variance component in the unbalanced random one-way model

AU - Lee, Juneyoung

AU - Khuri, André I.

AU - Kim, Kee Whan

PY - 2005/12/1

Y1 - 2005/12/1

N2 - The coverage probability of an approximate confidence interval on the among-group variance component, σα 2, in a one-way random model is modeled using generalized linear models techniques. The purpose of the proposed modeling is to derive an empirical relationship between the coverage probability on one hand, and k, n., φ, and the model's variance components on the other hand, where k is the number of groups, n is the total number of observations, and φ is a measure of imbalance for the design used. The latter quantities serve as control variables in the derived model, and the coverage probability is treated as the response variable. Contour plots generated from this model can be easily used to depict the effects of the control variables on the coverage probability. In particular, the plots are utilized to compare four methods for constructing approximate confidence intervals on σα 2. Additional advantages of the derived model include prediction of the coverage probability for a given method using only specified values of the control variables, and the determination of operating conditions that result in improved coverage probability within the region of interest.

AB - The coverage probability of an approximate confidence interval on the among-group variance component, σα 2, in a one-way random model is modeled using generalized linear models techniques. The purpose of the proposed modeling is to derive an empirical relationship between the coverage probability on one hand, and k, n., φ, and the model's variance components on the other hand, where k is the number of groups, n is the total number of observations, and φ is a measure of imbalance for the design used. The latter quantities serve as control variables in the derived model, and the coverage probability is treated as the response variable. Contour plots generated from this model can be easily used to depict the effects of the control variables on the coverage probability. In particular, the plots are utilized to compare four methods for constructing approximate confidence intervals on σα 2. Additional advantages of the derived model include prediction of the coverage probability for a given method using only specified values of the control variables, and the determination of operating conditions that result in improved coverage probability within the region of interest.

KW - Contour plots

KW - Generalized linear models

KW - Logarithmic link function

KW - Measure of imbalance

KW - Response surface methodology

KW - Unbalanced design

UR - http://www.scopus.com/inward/record.url?scp=33746090520&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746090520&partnerID=8YFLogxK

U2 - 10.1007/BF02789704

DO - 10.1007/BF02789704

M3 - Article

AN - SCOPUS:33746090520

VL - 20

SP - 275

EP - 294

JO - Computational Statistics

JF - Computational Statistics

SN - 0943-4062

IS - 2

ER -