Probability and Stochastic Processes

8.4 The Method of Moments

The method of moments is a very simple idea. Suppose that we observe from a distribution , where is the vector of parameter which may be d dimensional. The idea of this method is to match the empirical moments estimated from data with theoretical moments calculated using the distribution .

Obviously, the theoretical moments will need to exist, and one needs a minimum of d moments to obtain d equations to be able to estimate all the components of the parameter vector . An example of a distribution for which this method does not work is the Cauchy distribution since it has infinite theoretical moments.

Example 8.7

Suppose the random sample comes from a distribution where is the expected value of the distribution and is the variance. Estimating these parameters ...