The Annals of Statistics

Maximum Likelihood Estimates for a Bivariate Normal Distribution with Missing Data

Ram C. Dahiya and Ramesh M. Korwar

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 8, Number 3 (1980), 687-692.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345020

Digital Object Identifier
doi:10.1214/aos/1176345020

Mathematical Reviews number (MathSciNet)
MR568732

Zentralblatt MATH identifier
0435.62032

JSTOR
links.jstor.org

Subjects
Primary: 62F10: Point estimation
Secondary: 62H99: None of the above, but in this section

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

Citation

Dahiya, Ram C.; Korwar, Ramesh M. Maximum Likelihood Estimates for a Bivariate Normal Distribution with Missing Data. Ann. Statist. 8 (1980), no. 3, 687--692. doi:10.1214/aos/1176345020. https://projecteuclid.org/euclid.aos/1176345020


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