Theory and Methods of Statistics

5.5 Methods of Estimation

We have so far discussed the Rao-Blackwell method of finding UMVUEs and two methods of estimation in the general decision theoretic framework following the Bayesian principle and the principle of equivariance. Three other methods, such as,

(i) the method of maximum likelihood;

(ii) the method of moments; and

(iii) the method of minimum χ²,

will now be discussed, which are applicable in the context of parametric families.

The method of maximum likelihood was introduced by Fisher [20] who also laid the foundation of the theory of estimation and demonstrated the superiority of this method over the method of moments which was widely used for a long time until then. The method of minimum χ² has limited use only in the context ...