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

作者：Nogales A G^*; Perez P; Monfort P

来源：Alea (Rio de Janeiro): Latin American Journal of Probability and Mathematical Statistics , 2015, 12(1): 293-308.

• General half-normal distribution
• equivariance
• Monte Carlo approxmation of conditional expectations

This work addresses the problem of estimating the parameters of the general half-normal distribution. Namely, the problem of determining the minimum risk equivariant (MRE) estimators of the parameters is explored. Simulation studies are realized to compare the behavior of these estimators with maximum likelihood and unbiased estimators. A natural Monte Carlo method to compute conditional expectations is used to approximate the MRE estimation of the location parameter because its expression involves two conditional expectations not easily computables. The used Monte Carlo method is justified by a theorem of Besicovitch on differentiation of measures, and has been slightly modified to solve a sort of "curse of dimensionality" problem appearing in the estimation of this parameter. This method has been implicitly used in the last years in the context of ABC (approximate Bayesian computation) methods.

• 出版日期2015