Loss Reduction in Point Estimation Problems

Heike Hans-Dieter and Matei Demetrescu
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Heike Hans-Dieter: Statistik und Ökonometrie, Technische Universität Darmstadt, Germany

Stochastics and Quality Control, 2006, vol. 21, issue 2, 209-217

Abstract: When evaluating point estimators by means of general loss functions, the expected loss is not always minimal, similar to the case of mean-biased estimators, whose mean squared error can be reduced by accounting for the mean-bias. Depending on the loss function, the socalled Lehmann-bias can be significantly more important than the mean-bias of an estimator. Although a simple decomposition does not hold for expected losses as it does for the mean squared error, the expected loss can still be reduced by correcting for the Lehmann-bias. An asymptotic and a bootstrap-based correction are suggested and compared in small samples for the exponential distribution by means of Monte Carlo simulation.

Keywords: Loss function; Cost-of-error function; Estimation risk; Risk-bias; Asymptotics; Resampling (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1515/EQC.2006.209

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