### Abstract

It is often of interest to test the hypothesis that all off-diagonal elements of the correlation matrix of a multivariate normal distribution are equal. If the hypothesis of equal correlation can be accepted, it then may be of interest to estimate the common correlation coefficient. In this paper, four estimators of the common correlation are compared in terms of bias, variance, mean squared error, adequacy of the normal approximation, and ease of calculation. The average sample correlation is seen to be comparable to the other estimators and is recommended here since it is the easiest to calculate. The estimators are compared using simulation.

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

Pages (from-to) | 531-543 |

Number of pages | 13 |

Journal | Communications in Statistics - Simulation and Computation |

Volume | 15 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1986 |

Externally published | Yes |

### Fingerprint

### Keywords

- CPU time
- Fisher z-transform
- correlation matrix
- equicorrelation
- mean squared error
- normal approximation

### ASJC Scopus subject areas

- Statistics and Probability
- Modeling and Simulation

### Cite this

**A comparison of estimators of a common correlation coefficient.** / Looney, Stephen Warwick.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - A comparison of estimators of a common correlation coefficient

AU - Looney, Stephen Warwick

PY - 1986/1/1

Y1 - 1986/1/1

N2 - It is often of interest to test the hypothesis that all off-diagonal elements of the correlation matrix of a multivariate normal distribution are equal. If the hypothesis of equal correlation can be accepted, it then may be of interest to estimate the common correlation coefficient. In this paper, four estimators of the common correlation are compared in terms of bias, variance, mean squared error, adequacy of the normal approximation, and ease of calculation. The average sample correlation is seen to be comparable to the other estimators and is recommended here since it is the easiest to calculate. The estimators are compared using simulation.

AB - It is often of interest to test the hypothesis that all off-diagonal elements of the correlation matrix of a multivariate normal distribution are equal. If the hypothesis of equal correlation can be accepted, it then may be of interest to estimate the common correlation coefficient. In this paper, four estimators of the common correlation are compared in terms of bias, variance, mean squared error, adequacy of the normal approximation, and ease of calculation. The average sample correlation is seen to be comparable to the other estimators and is recommended here since it is the easiest to calculate. The estimators are compared using simulation.

KW - CPU time

KW - Fisher z-transform

KW - correlation matrix

KW - equicorrelation

KW - mean squared error

KW - normal approximation

UR - http://www.scopus.com/inward/record.url?scp=84950206590&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84950206590&partnerID=8YFLogxK

U2 - 10.1080/03610918608812523

DO - 10.1080/03610918608812523

M3 - Article

VL - 15

SP - 531

EP - 543

JO - Communications in Statistics: Simulation and Computation

JF - Communications in Statistics: Simulation and Computation

SN - 0361-0918

IS - 2

ER -