Let f (x) be a probability density function. The problem of estimating the functional ∫f2(x) dx by the Method of Frequency Moments is considered. An expression for the asymptotic mean squared error of the proposed estimator is given. The results are applied to the estimation of the reciprocal of the scale parameter in the Cauchy and Pareto distributions. An approximation for the bias in the Method of Frequency Moments is given, and a two step estimation procedure is discussed.
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