@article { ISI:000364259800035,
	title = {Robust tests for linear regression models based on tau-estimates},
	journal = {COMPUTATIONAL STATISTICS \& DATA ANALYSIS},
	volume = {93},
	number = {SI},
	year = {2016},
	month = {JAN},
	pages = {436-455},
	publisher = {ELSEVIER SCIENCE BV},
	type = {Article},
	address = {PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS},
	abstract = {<p>ANOVA tests are the standard tests to compare nested linear models fitted by least squares. These tests are equivalent to likelihood ratio tests, so they have high power. However, least squares estimators are very vulnerable to outliers in the data, and thus the related ANOVA type tests are also extremely sensitive to outliers. Therefore, robust estimators can be considered to obtain a robust alternative to the ANOVA tests. Regression tau-estimators combine high robustness with high efficiency which makes them suitable for robust inference beyond parameter estimation. Robust likelihood ratio type test statistics based on the tau-estimates of the error scale in the linear model are a natural alternative to the classical ANOVA tests. The higher efficiency of the tau-scale estimates compared with other robust alternatives is expected to yield tests with good power. Their null distribution can be estimated using either an asymptotic approximation or the fast and robust bootstrap. The robustness and power of the resulting robust likelihood ratio type tests for nested linear models is studied. (C) 2014 Elsevier B.V. All rights reserved.</p>
},
	keywords = {linear regression, Robust statistics, Robust tests},
	issn = {0167-9473},
	doi = {10.1016/j.csda.2014.09.012},
	author = {Salibian-Barrera, Mat{\'\i}as and Van Aelst, Stefan and Yohai, Victor J.}
}
@article { ISI:000238028100013,
	title = {Bootstrapping MM-estimators for linear regression with fixed designs},
	journal = {STATISTICS \& PROBABILITY LETTERS},
	volume = {76},
	number = {12},
	year = {2006},
	month = {JUL 1},
	pages = {1287-1297},
	publisher = {ELSEVIER SCIENCE BV},
	type = {Article},
	address = {PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS},
	abstract = {In this paper, I study the extension of the robust bootstrap [Salibian-Barrera, M., Zarnar, R.H., 2002. Bootstrapping robust estimates of regression. Ann. Statist. 30, 556-582] to the case of fixed designs. The robust bootstrap is a computer-intensive inference method for robust regression estimators which is computationally simple (because we do not need to recompute the robust estimate with each bootstrap sample) and robust to the presence of outliers in the bootstrap samples. In this paper, I prove the consistency of this method for the case of non-random explanatory variables and illustrate its use on a real data set. Simulation results indicate that confidence intervals based on the robust bootstrap have good finite-sample coverage levels. (C) 2006 Elsevier B.V. All rights reserved.},
	keywords = {bootstrap, fixed design, inference, linear regression, MM-estimators, Robustness},
	issn = {0167-7152},
	doi = {10.1016/j.spl.2006.01.008},
	author = {Salibian-Barrera, M}
}
@article { ISI:000238044400008,
	title = {A fast algorithm for S-regression estimates},
	journal = {JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS},
	volume = {15},
	number = {2},
	year = {2006},
	month = {JUN},
	pages = {414-427},
	publisher = {AMER STATISTICAL ASSOC},
	type = {Article},
	address = {1429 DUKE ST, ALEXANDRIA, VA 22314 USA},
	abstract = {<p>Equivariant high-breakdown point regression estimates are computationally expensive, and the corresponding algorithms become unfeasible for moderately large number of regressors. One important advance to improve the computational speed of one such estimator is the fast-LTS algorithm. This article proposes an analogous algorithm for computing S-estimates. The new algorithm, that we call {\textquoteleft}{\textquoteleft}fast-S{\textquoteright}{\textquoteright}, is also based on a {\textquoteleft}{\textquoteleft}local improvement{\textquoteright}{\textquoteright} step of the resampling initial candidates. This allows for a substantial reduction of the number of candidates required to obtain a good approximation to the optimal solution. We performed a simulation study which shows that S-estimators computed with the fast-S algorithm compare favorably to the LTS-estimators computed with the fast-LTS algorithm.</p>
},
	keywords = {high breakdown point, linear regression, Robustness},
	issn = {1061-8600},
	doi = {10.1198/106186006X113629},
	author = {Salibian-Barrera, M and Yohai, VJ}
}
