Maximum Likelihood Approach

The maximum likelihood (ML) approach is one of the most important statis-

tical methodologies for parameter estimation. It is based on the fundamental

assumption that the underlying probability distribution of the observations be-

longs to a family of distributions indexed by unknown parameters. The ML es-

timator of the unknown parameters is the maximizer of the likelihood function,

corresponding to the probability distribution in the family that gives the obser-

vations the highest chance of occurrence. In many cases, the ML estimator en-

joys an optimality property called asymptotic efficiency. A manifestation of this

property is that the asymptotic variance of the ML estimator attains the corre-

sponding CRLB in addition to having an asymptotic normal distribution.