Maximum-Likelihood Method

Abstract

The maximum-likelihood method offers a possibility to devise estimators of unknown population parameters by circumventing the calculation of expected values like average, variance and higher moments. The likelihood function is defined and its role in formulating the principle of maximum likelihood is elucidated. The variance and efficiency of maximum-likelihood estimators is discussed, in particular in the light of its information content and possible minimum variance bound. Likelihood intervals are introduced by analogy to the confidence intervals used in standard sample-based inference. The method is extended to the case when several parameters are determined simultaneously, and to likelihood regions as generalizations of likelihood intervals.