Abstract
Asymptotic biases and variances of M-, L- and R-estimators of a location parameter are compared under ε-contamination of the known error distribution F 0 by an unknown (and possibly asymmetric) distribution. For each ε-contamination neighborhood of F 0, the corresponding M-, L- and R-estimators which are asymptotically efficient at the least informative distribution are compared under asymmetric ε-contamination. Three scale-invariant versions of the M-estimator are studied: (i) one using the interquartile range as a preliminary estimator of scale: (ii) another using the median absolute deviation as a preliminary estimator of scale; and (iii) simultaneous M-estimation of location and scale by Huber's Proposal 2. A question considered for each case is: when are the maximal asymptotic biases and variances under asymmetric ε-contamination attained by unit point mass contamination at ∞? Numerical results for the case of the ε-contaminated normal distribution show that the L-estimators have generally better performance (for small to moderate values of ε) than all three of the scale-invariant M-estimators studied.
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Collins, J.R. Robustness Comparisons of Some Classes of Location Parameter Estimators. Annals of the Institute of Statistical Mathematics 52, 351–366 (2000). https://doi.org/10.1023/A:1004174024279
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DOI: https://doi.org/10.1023/A:1004174024279