Maximum Likelihood Estimators Under Continuity-Compactness Assumptions

Abstract

This work concerns with the consistency property of maximum likeli-hood estimators in a parametric statistical model. Assuming that the parameter space is compact and that the density function is Lipschitz continuous on the parameter, it is shown that the maximum likelihood technique generates estimators that, as the sample size increases, converge to the true parameter value with probability 1. The objective of the analysis is to illustrate the application of three basic statistical and analytical results: the law of large numbers, Jensen's inequality, and the Heine-Borel property of compact sets.