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Robustness of Regression M-Estimators Over Complex-valued Distributions,

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Noisy complex-valued data, for which robust regression techniques are the natural analysis approach, arise in many physical fields. Evaluation of the efficiency of such techniques requires that their behavior be charted over a series of known reference distributions. We have defined several symmetric long-tailed complex distributions e.g., complex slash, complex Cauchy, complex double exponential based on complex normal distribution. We have compared via the maximin method the robustness of different regression M-estimators as defined by their weight functions over these distributions. The variances of the estimators of the regression coefficients are obtained by simulation over all the distributions and for all the weight functions. The relative efficiencies over each distribution are obtained and then these relative efficiencies are compared over different distributions to identify the best weight function. Three different samples sizes 5, 11 and 15 have been used for this purpose. We apply our estimators to the evaluation of the Magnetotelluric response function.

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This article is from 'Computing Science and Statistics: Proceedings of the Symposium on the Interface Critical Applications of Scientific Computing: Biology, Engineering, Medicine, Speech Held in Seattle, Washington on 21-24 April 1991,' AD-A252 938, p125-128.




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