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This work addresses the problem of estimating the parameters of the generalhalf-normal distribution. Namely, the problem of determining the minimum riskequi\-va\-riant (MRE) estimators of the parameters is explored. Simulationstudies are realized to compare the behavior of these estimators with maximumlikelihood and unbiased estimators. A natural Monte Carlo method to computeconditional expectations is used to approximate the MRE estimation of thelocation parameter because its expression involves two conditional expectationsnot easily computables. The used Monte Carlo method is justified by a theoremof Besicovitch on differentiation of measures, and has been slightly modifiedto solve a sort of "curse of dimensionality" problem appearing in theestimation of this parameter. This method has been implicitly used in the lastyears in the context of ABC (approximate Bayesian computation) methods.

Minimum Risk Equivariant Estimation of the Parameters of the General  Half-Normal Distribution by Means of a Monte Carlo Method to Approximate  Conditional Expectations