Method of moments (statistics)
In statistics, the method of moments is a method of estimation of population parameters.
Method
Suppose that the problem is to estimate unknown parameters describing the distribution of the random variable . Suppose the first moments of the true distribution (the "population moments") can be expressed as functions of the s:
Suppose a sample of size is drawn, and it leads to the values . For , let
be the j-th sample moment, an estimate of . The method of moments estimator for denoted by is defined as the solution (if there is one) to the equations:
Reasons to use it
The method of moments is simple and gets consistent estimators (under very weak assumptions). However, these estimators are often biased.
References
Statistics