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

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

Journal of Applied Statistics, 2015, vol. 42, issue 6, 1306-1321

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.

Date: 2015
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DOI: 10.1080/02664763.2014.999650

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