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

Category:Statistics