### 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 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Agricultural and Biological Sciences(all)
- Public Health, Environmental and Occupational Health
- Agricultural and Biological Sciences (miscellaneous)
- Applied Mathematics
- Statistics and Probability

### Cite this

*Biometrics*,

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

**Estimation for a common correlation coefficient in bivariate normal distributions with missing observations.** / Minami, Mihoko; Shimizu, Kunio.

Research output: Contribution to journal › Article

*Biometrics*, vol. 54, no. 3, pp. 1136-1146. https://doi.org/10.2307/2533863

}

TY - JOUR

T1 - Estimation for a common correlation coefficient in bivariate normal distributions with missing observations

AU - Minami, Mihoko

AU - Shimizu, Kunio

PY - 1998/9

Y1 - 1998/9

N2 - 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.

AB - 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.

KW - Asymptotic variance

KW - Fisher information matrix

KW - Maximum likelihood estimate

KW - Re-stricted maximum likelihood estimate

KW - Variance-stabilizing transformation

UR - http://www.scopus.com/inward/record.url?scp=0031712556&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031712556&partnerID=8YFLogxK

U2 - 10.2307/2533863

DO - 10.2307/2533863

M3 - Article

AN - SCOPUS:0031712556

VL - 54

SP - 1136

EP - 1146

JO - Biometrics

JF - Biometrics

SN - 0006-341X

IS - 3

ER -