Method of moments (statistics)

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

Method[change | change source]

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 | change source]

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

References[change | change source]

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