## The Annals of Statistics

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

#### 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

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