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Semiparametrically weighted robust estimation of regression models

  • Cízek, Pavel

A class of two-step robust regression estimators that achieve a high relative efficiency for data from light-tailed, heavy-tailed, and contaminated distributions irrespective of the sample size is proposed and studied. In particular, the least weighted squares (LWS) estimator is combined with data-adaptive weights, which are determined from the empirical distribution or quantile functions of regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the LWS estimator with the proposed weights preserves robust properties of the initial robust estimate. However, contrary to the existing methods and despite the data-dependent weights, the first-order asymptotic behavior of LWS is fully independent of the initial estimate under mild conditions. Moreover, the proposed estimation method is asymptotically efficient if errors are normally distributed. A simulation study documents these theoretical properties in finite samples; in particular, the relative efficiency of LWS with the proposed weighting schemes can reach 85%-100% in samples of several tens of observations under various distributional models.

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Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 55 (2011)
Issue (Month): 1 (January)
Pages: 774-788

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Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:774-788
Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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