### Abstract

Using normal distribution assumptions, one can obtain confidence intervals for variance components in a variety of applications. A normal-based interval, which has exact coverage probability under normality, is usually constructed from a pivot so that the endpoints of the interval depend on the data as well as the distribution of the pivotal quantity. Alternatively, one can employ a point estimation technique to form a large-sample (or approximate) confidence interval. A commonly used approach to estimate variance components is the restricted maximum likelihood (REML) method. The endpoints of a REML-based confidence interval depend on the data and the asymptotic distribution of the REML estimator. In this paper, simulation studies are conducted to evaluate the performance of the normal-based and the REML-based intervals for the intraclass correlation coefficient under non-normal distribution assumptions. Simulated coverage probabilities and expected lengths provide guidance as to which interval procedure is favored for a particular scenario. Estimating the kurtosis of the underlying distribution plays a central role in implementing the REML-based procedure. An empirical example is given to illustrate the usefulness of the REML-based confidence intervals under non-normality.

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

Pages (from-to) | 1018-1028 |

Number of pages | 11 |

Journal | Computational Statistics and Data Analysis |

Volume | 55 |

Issue number | 2 |

DOIs | |

State | Published - Feb 1 2011 |

### Fingerprint

### Keywords

- Asymptotic distributions
- Kurtosis
- One-way random effects model
- Pivotal quantity

### ASJC Scopus subject areas

- Computational Mathematics
- Computational Theory and Mathematics
- Statistics and Probability
- Applied Mathematics

### Cite this

**Assessing the performance of normal-based and REML-based confidence intervals for the intraclass correlation coefficient.** / Burch, Brent D.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Assessing the performance of normal-based and REML-based confidence intervals for the intraclass correlation coefficient

AU - Burch, Brent D

PY - 2011/2/1

Y1 - 2011/2/1

N2 - Using normal distribution assumptions, one can obtain confidence intervals for variance components in a variety of applications. A normal-based interval, which has exact coverage probability under normality, is usually constructed from a pivot so that the endpoints of the interval depend on the data as well as the distribution of the pivotal quantity. Alternatively, one can employ a point estimation technique to form a large-sample (or approximate) confidence interval. A commonly used approach to estimate variance components is the restricted maximum likelihood (REML) method. The endpoints of a REML-based confidence interval depend on the data and the asymptotic distribution of the REML estimator. In this paper, simulation studies are conducted to evaluate the performance of the normal-based and the REML-based intervals for the intraclass correlation coefficient under non-normal distribution assumptions. Simulated coverage probabilities and expected lengths provide guidance as to which interval procedure is favored for a particular scenario. Estimating the kurtosis of the underlying distribution plays a central role in implementing the REML-based procedure. An empirical example is given to illustrate the usefulness of the REML-based confidence intervals under non-normality.

AB - Using normal distribution assumptions, one can obtain confidence intervals for variance components in a variety of applications. A normal-based interval, which has exact coverage probability under normality, is usually constructed from a pivot so that the endpoints of the interval depend on the data as well as the distribution of the pivotal quantity. Alternatively, one can employ a point estimation technique to form a large-sample (or approximate) confidence interval. A commonly used approach to estimate variance components is the restricted maximum likelihood (REML) method. The endpoints of a REML-based confidence interval depend on the data and the asymptotic distribution of the REML estimator. In this paper, simulation studies are conducted to evaluate the performance of the normal-based and the REML-based intervals for the intraclass correlation coefficient under non-normal distribution assumptions. Simulated coverage probabilities and expected lengths provide guidance as to which interval procedure is favored for a particular scenario. Estimating the kurtosis of the underlying distribution plays a central role in implementing the REML-based procedure. An empirical example is given to illustrate the usefulness of the REML-based confidence intervals under non-normality.

KW - Asymptotic distributions

KW - Kurtosis

KW - One-way random effects model

KW - Pivotal quantity

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UR - http://www.scopus.com/inward/citedby.url?scp=78049311678&partnerID=8YFLogxK

U2 - 10.1016/j.csda.2010.08.007

DO - 10.1016/j.csda.2010.08.007

M3 - Article

VL - 55

SP - 1018

EP - 1028

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

IS - 2

ER -