Semiparametrically weighted robust estimation of regression models

Research output: Contribution to journalArticleScientificpeer-review

Abstract

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
Volume55
Issue number1
Publication statusPublished - 2011

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Robust Estimation
Weighted Least Squares Estimator
Regression Model
Relative Efficiency
Weighted Least Squares
Robust Estimate
Robust Regression
Quantile Function
Empirical Distribution Function
Two-step Method
Robust Estimators
Regression Estimator
Dependent Data
Robust Methods
Weighting
High Efficiency
Sample Size
Regression
Asymptotic Behavior
Simulation Study

Cite this

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title = "Semiparametrically weighted robust estimation of regression models",
abstract = "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.",
author = "P. Cizek",
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Semiparametrically weighted robust estimation of regression models. / Cizek, P.

In: Computational Statistics & Data Analysis, Vol. 55, No. 1, 2011, p. 774-788.

Research output: Contribution to journalArticleScientificpeer-review

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AB - 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.

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