Asymptotic Properties of Maximum Likelihood Estimators for the Independent Not Identically Distributed Case
Open Access
- 1 December 1971
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Mathematical Statistics
- Vol. 42 (6), 1977-1991
- https://doi.org/10.1214/aoms/1177693066
Abstract
Conditions are established under which maximum likelihood estimators are consistent and asymptotically normal in the case where the observations are independent but not identically distributed. The key concept employed is uniform integrability; and the required convergence theorems which involve uniform integrability, and are of independent interest, appear in the appendix. A motivational example involving estimation under variable censoring is presented. This example invokes the full generality of the theorems with regard to lack of i.i.d. and lack of densities $\operatorname{wrt}$ Lebesgue or counting measure.