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Robust estimation of scale of an exponential distribution

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  • U. Gather
  • V. Schultze

Abstract

We consider the standardized median as an estimator of scale for exponential samples which is most B‐robust in the sense of Hampel et al. (1986). This estimator is compared with two other estimators which were proposed to Rousseeuw and Croux (1993) but for a Gaussian model. All three estimators have the same breakdown point, but their bias curves are different. It is shown that under a gross error model the explosion bias curve of the most B‐robust estimator performs better than the bias curves of the other estimators. But this estimator is worse than the two estimators proposed by Rousseeuw and Croux (1993) if the implosion bias curve is considered.

Suggested Citation

  • U. Gather & V. Schultze, 1999. "Robust estimation of scale of an exponential distribution," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 53(3), pages 327-341, November.
    • Handle: RePEc:bla:stanee:v:53:y:1999:i:3:p:327-341
    DOI: 10.1111/1467-9574.00115
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    Cited by:

    1. Theis, Winfried & Weihs, Claus, 2004. "Determination of Relevant Frequencies and Modeling Varying Amplitudes of Harmonic Processes," Technical Reports 2004,68, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Gather, Ursula & Davies, P. Laurie, 2004. "Robust Statistics," Papers 2004,20, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    3. Pawlitschko, Jörg, 2001. "Robust estimation of the location parameter from a two-parameter exponential distribution," Technical Reports 2001,36, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. Asimit, Alexandru V. & Badescu, Alexandru M. & Verdonck, Tim, 2013. "Optimal risk transfer under quantile-based risk measurers," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 252-265.

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