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.
Publié le : 1980-05-14
Classification:
Bivariate normal distribution,
difference of two means,
maximum likelihood estimation,
missing data,
unbiased estimators,
uniqueness of maximum likelihood estimators,
62F10,
62H99
@article{1176345020,
author = {Dahiya, Ram C. and Korwar, Ramesh M.},
title = {Maximum Likelihood Estimates for a Bivariate Normal Distribution with Missing Data},
journal = {Ann. Statist.},
volume = {8},
number = {1},
year = {1980},
pages = { 687-692},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345020}
}
Dahiya, Ram C.; Korwar, Ramesh M. Maximum Likelihood Estimates for a Bivariate Normal Distribution with Missing Data. Ann. Statist., Tome 8 (1980) no. 1, pp. 687-692. http://gdmltest.u-ga.fr/item/1176345020/