Efficient Robust Estimation of Regression Models (Revision of DP 2006-08)

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This paper introduces a new class of robust regression estimators. The proposed twostep least weighted squares (2S-LWS) estimator employs data-adaptive weights determined from the empirical distribution, quantile, or density functions of regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the proposed 2S-LWS estimator preserves robust properties of the initial robust estimate. However contrary to existing methods, the first-order asymptotic behavior of 2S-LWS is fully independent of the initial estimate under mild conditions; most importantly, the initial estimator does not need to be pn consistent. Moreover, we prove that 2S-LWS is asymptotically normal under B-mixing conditions and asymptotically efficient if errors are normally distributed. A simulation study documents these theoretical properties in finite samples; in particular, the relative efficiency of 2S-LWS can reach 85–90% in samples of several tens of observations under various distributional models.
Original languageEnglish
Place of PublicationTilburg
Number of pages41
Publication statusPublished - 2007

Publication series

NameCentER Discussion Paper


  • asymptotic efficiency
  • breakdown point
  • least weighted squares


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