On Equivariant Estimation of the Parameters of the General Half-Normal Distribution Making Use of a Monte Carlo Method to Approximate Conditional Expectations

by A.G. Nogales, P. Pérez and P. Monfort.

Abstract: 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 justi ed by a theorem of Besicovitch on di erentiation of measures, and has been slightly modi ed to solve a sort of \curse of dimensionality" problem appearing in the estimation of this parameter.

Key Words: Monte Carlo simulation, conditional expectation, general half-normal distribution, equivariant estimation

Authors:
A.G. Nogales, nogales@unex.es
P. Pérez, paloma@unex.es
P. Monfort, pabmonf@unex.es

Editor: Joseph W McKean, joseph.mckean@wmich.edu

Note: This article was revised on May 16, 2014.

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