Method of Moments---I

• This is a simple and, in general, non-optimal method.

• Even here---for more than one parameter---there are two versions

  (a) ignore correlations (used in practice but wrong) and

  (b) include correlations (best of a bad lot!). Of course, simplicity can lead to huge savings in computer time, and so it should not be sneered at.

• The basic idea of method of moments is simple:

  Consider a set of observations , then central limit theorem implies

  

  where

  

• Here, is where is some unknown parameter. So putting

  

• gives one displaymath for with solution :

  is the moment estimate of .