Efficient Robust Estimation of Regression Models (Revision of DP 2006-08)
AbstractThis 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.
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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2007-87.
Date of creation: 2007
Date of revision:
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Web page: http://center.uvt.nl
asymptotic efficiency; breakdown point; least weighted squares;
Find related papers by JEL classification:
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
- C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-11-10 (All new papers)
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- Zinde-Walsh, Victoria, 2002. "Asymptotic Theory For Some High Breakdown Point Estimators," Econometric Theory, Cambridge University Press, vol. 18(05), pages 1172-1196, October.
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