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

Research output: Contribution to journalArticleScientificpeer-review

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
Pages (from-to)514-533
JournalTest
Volume22
Issue number3
DOIs
Publication statusPublished - 2013

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Least Trimmed Squares
Estimator
Robust Estimators
Alternatives
Robust Estimate
Robust Regression
Serial Correlation
Two-step Method
Heteroscedasticity
Regression Estimator
Dependent Data
Robust Methods
Asymptotic distribution
Asymmetry
Rate of Convergence
Asymptotic Behavior
Simulation Study
First-order
Estimate
Range of data

Cite this

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title = "Reweighted least trimmed squares: an alternative to one-step estimators",
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.",
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Reweighted least trimmed squares : an alternative to one-step estimators. / Cizek, P.

In: Test, Vol. 22, No. 3, 2013, p. 514-533.

Research output: Contribution to journalArticleScientificpeer-review

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T2 - an alternative to one-step estimators

AU - Cizek, P.

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AB - 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.

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DO - 10.1007%2fs11749-013-0335-5#

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