= Method of moments
{disambiguate=statistics}
{title2=$m_j(\widehat\theta)=\widehat m_j$}
A method-of-moments <estimator> equates selected theoretical <moments> $m_j(\theta)$ to corresponding empirical moment estimates and solves for the parameter. For a distribution with mean $\mu$ and variance $\sigma^2$, the first two raw moment equations give $\widehat\mu=\overline X$ and $\widehat{\sigma^2}=n^{-1}\sum_iX_i^2-\overline X^2$. Existence, uniqueness and consistency require appropriate identifiability and moment assumptions; unbiased empirical moments do not make nonlinear parameter estimates unbiased. This statistical estimation procedure differs from the <method of moments in probability> for proving convergence in distribution.
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