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Robustness of the Simultaneous Estimators of Location and Scale From Approximating a Histogram by a Normal Density Curve

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  • A. S. Hedayat
  • Guoqin Su

Abstract

The robust properties of the simultaneous estimators of location and scale parameters (μ*, σ*) proposed by Brown and Hwang are studied. As a pair of simultaneous M estimators of location and scale, their asymptotic efficiencies (0.650 for μ* and 0.541 for σ*) are higher than those for median (0.637) and median absolute deviation (0.368) under the normal distribution. Simulation indicates that the distributions of and are much flatter than those based on the sample mean and the sample standard deviation under the normal distribution when the sample size is small.

Suggested Citation

  • A. S. Hedayat & Guoqin Su, 2012. "Robustness of the Simultaneous Estimators of Location and Scale From Approximating a Histogram by a Normal Density Curve," The American Statistician, Taylor & Francis Journals, vol. 66(1), pages 25-33, February.
    • Handle: RePEc:taf:amstat:v:66:y:2012:i:1:p:25-33
    DOI: 10.1080/00031305.2012.663665
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    References listed on IDEAS

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    1. A. M. Gross, 1973. "A Monte Carlo Swindle for Estimators of Location," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 22(3), pages 347-353, November.
    2. Gary Simon, 1976. "Computer Simulation Swindles, with Applications to Estimates of Location and Dispersion," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 25(3), pages 266-274, November.
    3. Stigler, Stephen M., 2010. "The Changing History of Robustness," The American Statistician, American Statistical Association, vol. 64(4), pages 277-281.
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