The total bootstrap median: a robust and efficient estimator of location and scale for small samples |
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Authors: | Peter A. Dowd Eulogio Pardo-Igúzquiza Juan José Egozcue |
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Affiliation: | 1. Faculty of Engineering, Computer and Mathematical Sciences, University of Adelaide, Adelaide, SA 5005, Australiapeter.dowd@adelaide.edu.au;3. Instituto Geológico y Minero de Espa?a, Calle Ríos Rosas, 23, Madrid, Spain;4. Departamento de Matemática Aplicada III, Universidad Politécnica de Catalunya, Barcelona, Spain |
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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. |
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Keywords: | L-estimator mean square error influence function standard error empirical distribution small samples |
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