### Abstract

The maximum likelihood (ML) estimate and the restricted or residual maximum likelihood (REML) estimate are considered for a common correlation coefficient among several bivariate normal distributions with different variances when some observations on either of the variables are missing. The use of incomplete data in ML and REML estimation reduces mean squared errors of the correlation estimates. Reduction is large when the absolute value of a common correlation is large or numbers of paired observations are small. An example and some simulation results are given to illustrate the characteristics of the estimates.

Original language | English |
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Pages (from-to) | 1136-1146 |

Number of pages | 11 |

Journal | Biometrics |

Volume | 54 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1998 Sep 1 |

Externally published | Yes |

### Keywords

- Asymptotic variance
- Fisher information matrix
- Maximum likelihood estimate
- Re-stricted maximum likelihood estimate
- Variance-stabilizing transformation

### ASJC Scopus subject areas

- Statistics and Probability
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics

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## Cite this

Minami, M., & Shimizu, K. (1998). Estimation for a common correlation coefficient in bivariate normal distributions with missing observations.

*Biometrics*,*54*(3), 1136-1146. https://doi.org/10.2307/2533863