Method of moments (statistics)

parameter estimation technique in statistics

In statistics, the method of moments is a method of estimation of population parameters.

Method change

Suppose that the problem is to estimate   unknown parameters   describing the distribution   of the random variable  .[1] 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:[source?]

 

Reasons to use it change

The method of moments is simple and gets consistent estimators (under very weak assumptions). However, these estimators are often biased.

References change

  1. K. O. Bowman and L. R. Shenton, "Estimator: Method of Moments", pp 2092–2098, Encyclopedia of statistical sciences, Wiley (1998).