Semiparametrically weighted robust estimation of regression models

Research output: Contribution to journalArticleScientificpeer-review

19 Citations (Scopus)


A class of two-step robust regression estimators that achieve a high relative efficiency for data from light-tailed, heavy-tailed, and contaminated distributions irrespective of the sample size is proposed and studied. In particular, the least weighted squares (LWS) estimator is combined with data-adaptive weights, which are determined from the empirical distribution or quantile functions of regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the LWS estimator with the proposed weights preserves robust properties of the initial robust estimate. However, contrary to the existing methods and despite the data-dependent weights, the first-order asymptotic behavior of LWS is fully independent of the initial estimate under mild conditions. Moreover, the proposed estimation method is asymptotically efficient if errors are normally distributed. A simulation study documents these theoretical properties in finite samples; in particular, the relative efficiency of LWS with the proposed weighting schemes can reach 85%–100% in samples of several tens of observations under various distributional models.
Original languageEnglish
Pages (from-to)774-788
JournalComputational Statistics & Data Analysis
Issue number1
Publication statusPublished - 2011


Dive into the research topics of 'Semiparametrically weighted robust estimation of regression models'. Together they form a unique fingerprint.

Cite this