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Loss Reduction in Point Estimation Problems

Author

Listed:
  • Heike Hans-Dieter

    (Statistik und Ökonometrie, Technische Universität Darmstadt, Germany)

  • Demetrescu Matei

    (Statistik und Methoden der Ökonometrie, Goethe-Universität Frankfurt, Germany)

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.

Suggested Citation

  • Heike Hans-Dieter & Demetrescu Matei, 2006. "Loss Reduction in Point Estimation Problems," Stochastics and Quality Control, De Gruyter, vol. 21(2), pages 209-217, January.
    • Handle: RePEc:bpj:ecqcon:v:21:y:2006:i:2:p:209-217:n:4
    DOI: 10.1515/EQC.2006.209
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    References listed on IDEAS

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    4. Rao G. Srinivasa & Kantam R. R. L., 2004. "A Note on Point Estimation of System Reliability Exemplified for the Log-Logistic Distribution," Stochastics and Quality Control, De Gruyter, vol. 19(2), pages 197-204, January.
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