Distortion sensitivity of estimators of location

Demetris Athienitis and Ronald Randles

Journal of Nonparametric Statistics, 2013, vol. 25, issue 3, 597-617

Abstract: Robustness measures and procedures have traditionally been developed and implemented through the contamination model of Hampel et al. [2005, Robust Statistics: The Approach Based on Influence Functions, Wiley Series in Probability and Statistics (Vol. 114), New York: Wiley]. We present a distortion model that takes a symmetric probability density function and skews it infinitesimally in a specific direction thereby distorting every realisation of the distribution, a model based upon the work of Fechner [1897, 'Th.(1897)', in Kollektivmasslehre , Leipzig: Engelman]. Robustness to distortion of a symmetric signal is determined as the rate of change of the functional of an affine-equivariant location estimator under the Fechner model. The mean, median and Hodges-Lehman estimators are compared under this model.

Date: 2013
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DOI: 10.1080/10485252.2013.787423

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