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May, 1980 Maximum Likelihood Estimates for a Bivariate Normal Distribution with Missing Data
Ram C. Dahiya, Ramesh M. Korwar
Ann. Statist. 8(3): 687-692 (May, 1980). DOI: 10.1214/aos/1176345020


The maximum likelihood estimators (m.l.e.) are obtained for the parameters of a bivariate normal distribution with equal variances when some of the observations are missing on one of the variables. The likelihood equation for estimating $\rho$, the correlation coefficient, may have multiple roots but a result proved here provides a unique root which is the m.l.e. of $\rho$. The problem of estimating the difference $\delta$ of the two means is also considered and it is shown that the m.l.e. of $\delta$ is unbiased.


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Ram C. Dahiya. Ramesh M. Korwar. "Maximum Likelihood Estimates for a Bivariate Normal Distribution with Missing Data." Ann. Statist. 8 (3) 687 - 692, May, 1980.


Published: May, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0435.62032
MathSciNet: MR568732
Digital Object Identifier: 10.1214/aos/1176345020

Primary: 62F10
Secondary: 62H99

Keywords: Bivariate normal distribution , difference of two means , maximum likelihood estimation , missing data , unbiased estimators , uniqueness of maximum likelihood estimators

Rights: Copyright © 1980 Institute of Mathematical Statistics


Vol.8 • No. 3 • May, 1980
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