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The total bootstrap median: a robust and efficient estimator of location and scale for small samples

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  • Peter A. Dowd
  • Eulogio Pardo-Igúzquiza
  • Juan Jos� Egozcue

Abstract

We propose the total bootstrap median (TBM) as a robust and efficient estimator of location and scale for small samples. We demonstrate its performance by estimating the mean and variance of a variety of distributions. We also show that, if the underlying distribution is unknown and there is either no contamination or low to moderate contamination, the TBM provides a better estimate of the mean, in mean square terms, than the sample mean or the sample median. In addition, the TBM is a better estimator of the variance of the underlying distribution than the sample variance or the square of the bias-corrected median absolute deviation from the median estimator. We also show that the TBM is an explicit L-estimator, which allows a direct study of its properties.

Suggested Citation

  • Peter A. Dowd & Eulogio Pardo-Igúzquiza & Juan Jos� Egozcue, 2015. "The total bootstrap median: a robust and efficient estimator of location and scale for small samples," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(6), pages 1306-1321, June.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:6:p:1306-1321
    DOI: 10.1080/02664763.2014.999650
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