Reweighted Least Trimmed Squares: An Alternative to One-Step Estimators

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Abstract

A new class of robust regression estimators is proposed that forms an alternative to traditional robust one-step estimators and that achieves the √n rate of convergence irrespective of the initial estimator under a wide range of distributional assumptions. The proposed reweighted least trimmed squares (RLTS) estimator employs data-dependent weights determined from an initial robust fit. Just like many existing one- and two-step robust methods, the RLTS estimator preserves robust properties of the initial robust estimate. However contrary to existing methods, the first-order asymptotic behavior of RLTS is independent of the initial estimate even if errors exhibit heteroscedasticity, asymmetry, or serial correlation. Moreover, we derive the asymptotic distribution of RLTS and show that it is asymptotically efficient for normally distributed errors. A simulation study documents benefits of these theoretical properties in finite samples.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages35
Volume2010-91
Publication statusPublished - 2010

Publication series

NameCentER Discussion Paper
Volume2010-91

Keywords

  • asymptotic efficiency
  • breakdown point
  • least trimmed squares

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    Cizek, P. (2010). Reweighted Least Trimmed Squares: An Alternative to One-Step Estimators. (CentER Discussion Paper; Vol. 2010-91). Econometrics.