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.
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 justied by a theorem of Besicovitch on dierentiation of measures, and has been slightly
modied to solve a sort of \curse of dimensionality" problem appearing in the estimation
of this parameter.
Monte Carlo simulation, conditional expectation, general half-normal
distribution, equivariant estimation
A.G. Nogales, email@example.com
P. Pérez, firstname.lastname@example.org
P. Monfort, email@example.com
Joseph W McKean, firstname.lastname@example.org
Note: This article was revised on May 16, 2014.
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