A method-of-moments estimator equates selected theoretical moments to corresponding empirical moment estimates and solves for the parameter. For a distribution with mean and variance , the first two raw moment equations give and . 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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The Method of Moments is a statistical technique used for estimating population parameters (such as means, variances, etc.) by equating sample moments to theoretical moments derived from a probability distribution. This method is commonly employed when fitting a statistical model to data. Here's a brief overview of how the Method of Moments works: 1. **Moments Definition**: Moments are quantitative measures that can describe the shape of a probability distribution.