## The Annals of Statistics

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

### Maximum Likelihood Estimates for a Bivariate Normal Distribution with Missing Data

Ram C. Dahiya and Ramesh M. Korwar

#### 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