Reweighted least trimmed squares: an alternative to one-step estimators

A new class of robust regression estimators is proposed that forms an alternative to traditional robust one-step estimators and that achieves the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\sqrt{n}$</EquationSource> </InlineEquation> 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. Copyright Sociedad de Estadística e Investigación Operativa 2013