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

Listed:
• Pavel Čížek

()

## Abstract

A new class of robust regression estimators is proposed that forms an alternative to traditional robust one-step estimators and that achieves the $\sqrt{n}$ 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. Copyright Sociedad de Estadística e Investigación Operativa 2013

## Suggested Citation

• Pavel Čížek, 2013. "Reweighted least trimmed squares: an alternative to one-step estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 514-533, September.
• Handle: RePEc:spr:testjl:v:22:y:2013:i:3:p:514-533
DOI: 10.1007/s11749-013-0335-5
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File URL: http://hdl.handle.net/10.1007/s11749-013-0335-5

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## References listed on IDEAS

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## Citations

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Cited by:

1. Marco Riani & Andrea Cerioli & Francesca Torti, 2014. "On consistency factors and efficiency of robust S-estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 356-387, June.
2. Silvia Salini & Andrea Cerioli & Fabrizio Laurini & Marco Riani, 2016. "Reliable Robust Regression Diagnostics," International Statistical Review, International Statistical Institute, vol. 84(1), pages 99-127, April.

### Keywords

Asymptotic efficiency; Breakdown point; Least trimmed squares; Linear regression; 62F10; 62F12; 62F35; 62J05;

### JEL classification:

• C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
• C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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