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

TL;DR

This paper develops a Monte Carlo approach to estimate parameters of the general half-normal distribution using minimum risk equivariant estimators, comparing their performance with traditional estimators through simulation.

Contribution

It introduces a Monte Carlo method based on measure differentiation to approximate complex conditional expectations in MRE estimation of the half-normal distribution parameters.

Findings

Monte Carlo method effectively approximates MRE estimators

Comparison shows MRE estimators perform favorably

Method addresses computational challenges in parameter estimation

Abstract

This work addresses the problem of estimating the parameters of the general half-normal distribution. Namely, the problem of determining the minimum risk equi\-va\-riant (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.