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

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  • Cizek, P.

    (Tilburg University, Center for Economic Research)

Abstract

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.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2007-87.

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Date of creation: 2007
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Handle: RePEc:dgr:kubcen:200787

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Web page: http://center.uvt.nl

Related research

Keywords: asymptotic efficiency; breakdown point; least weighted squares;

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  1. van Dijk, D.J.C. & Franses, Ph.H.B.F. & Lucas, A., 1996. "Testing for ARCH in the Presence of Additive Outliers," Econometric Institute Research Papers EI 9659-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  2. Zinde-Walsh, Victoria, 2002. "Asymptotic Theory For Some High Breakdown Point Estimators," Econometric Theory, Cambridge University Press, vol. 18(05), pages 1172-1196, October.
  3. Jonathan R. W. Temple, 1998. "Robustness tests of the augmented Solow model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(4), pages 361-375.
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