@article { ISI:000281333900020,
	title = {Fast robust estimation of prediction error based on resampling},
	journal = {COMPUTATIONAL STATISTICS \& DATA ANALYSIS},
	volume = {54},
	number = {12, SI},
	year = {2010},
	month = {DEC 1},
	pages = {3121-3130},
	publisher = {ELSEVIER SCIENCE BV},
	type = {Article},
	address = {PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS},
	abstract = {Robust estimators of the prediction error of a linear model are proposed. The estimators are based on the resampling techniques cross-validation and bootstrap. The robustness of the prediction error estimators is obtained by robustly estimating the regression parameters of the linear model and by trimming the largest prediction errors. To avoid the recalculation of time-consuming robust regression estimates, fast approximations for the robust estimates of the resampled data are used. This leads to time-efficient and robust estimators of prediction error. (C) 2010 Elsevier B.V. All rights reserved.},
	keywords = {bootstrap, Cross-validation, Prediction error, Robustness},
	issn = {0167-9473},
	doi = {10.1016/j.csda.2010.01.031},
	author = {Khan, Jafar A. and Van Aelst, Stefan and Zamar, Ruben H.}
}
@article { ISI:000254995100003,
	title = {Fast and robust bootstrap},
	journal = {STATISTICAL METHODS AND APPLICATIONS},
	volume = {17},
	number = {1},
	year = {2008},
	pages = {41-71},
	publisher = {SPRINGER HEIDELBERG},
	type = {Article},
	address = {TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY},
	abstract = {<p>In this paper we review recent developments on a bootstrap method for robust estimators which is computationally faster and more resistant to outliers than the classical bootstrap. This fast and robust bootstrap method is, under reasonable regularity conditions, asymptotically consistent. We describe the method in general and then consider its application to perform inference based on robust estimators for the linear regression and multivariate location-scatter models. In particular, we study confidence and prediction intervals and tests of hypotheses for linear regression models, inference for location-scatter parameters and principal components, and classification error estimation for discriminant analysis.</p>
},
	keywords = {bootstrap, PCA discriminant analysis, Robust inference, Robust regression},
	issn = {1618-2510},
	doi = {10.1007/s10260-007-0048-6},
	author = {Salibian-Barrera, Mat{\'\i}as and Van Aelst, Stefan and Willerns, Gert}
}
@article { ISI:000251829200023,
	title = {Robust linear model selection based on least angle regression},
	journal = {JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION},
	volume = {102},
	number = {480},
	year = {2007},
	month = {DEC},
	pages = {1289-1299},
	publisher = {AMER STATISTICAL ASSOC},
	type = {Article},
	address = {1429 DUKE ST, ALEXANDRIA, VA 22314 USA},
	abstract = {In this article we consider the problem of building a linear prediction model when the number of candidate predictors is large and the data possibly contain anomalies that are difficult to visualize and clean. We want to predict the nonoutlying cases; therefore, we need a method that is simultaneously robust and scalable. We consider the stepwise least angle regression (LARS) algorithm which is computationally very efficient but sensitive to outliers. We introduce two different approaches to robustify LARS. The plug-in approach replaces the classical correlations in LARS by robust correlation estimates. The cleaning approach first transforms the data set by shrinking the outliers toward the bulk of the data (which we call multivariate Winsorization) and then applies LARS to the transformed data. We show that the plug in approach is time-efficient and scalable and that the bootstrap can be used to stabilize its results. We recommend using bootstrapped robustified LARS to sequence a number of candidate predictors to form a reduced set from which a more refined model can be selected.},
	keywords = {bootstrap, computational complexity, robust prediction, stepwise algorithm, Winsorization},
	issn = {0162-1459},
	doi = {10.1198/016214507000000950},
	author = {Khan, Jafar A. and Van Aelst, Stefan and Zamar, Ruben H.}
}
@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:000240158700035,
	title = {Principal components analysis based on multivariate MM estimators with fast and robust bootstrap},
	journal = {JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION},
	volume = {101},
	number = {475},
	year = {2006},
	month = {SEP},
	pages = {1198-1211},
	publisher = {AMER STATISTICAL ASSOC},
	type = {Article},
	address = {1429 DUKE ST, ALEXANDRIA, VA 22314 USA},
	abstract = {We consider robust principal components analysis (PCA) based on multivariate MM estimators. We first study the robustness and efficiency of these estimators, particularly in terms of eigenvalues and eigenvectors. We then focus on inference procedures based on a fast and robust bootstrap for MM estimators. This method is an alternative to the approach based on the asymptotic distribution of the estimators and can also be used to assess the stability of the principal components. A formal consistency proof for the bootstrap method is given, and its finite-sample performance is investigated through simulations. We illustrate the use of the robust PCA and the bootstrap inference on a real dataset.},
	keywords = {bootstrap, inference, MM-estimators, Principal components, Robustness},
	issn = {0162-1459},
	doi = {10.1198/016214506000000096},
	author = {Salibian-Barrera, Mat{\'\i}as and Van Aelst, Stefan and Willems, Gert}
}
@article { ISI:000225197800015,
	title = {Estimating the p-values of robust tests for the linear model},
	journal = {JOURNAL OF STATISTICAL PLANNING AND INFERENCE},
	volume = {128},
	number = {1},
	year = {2005},
	month = {JAN 15},
	pages = {241-257},
	publisher = {ELSEVIER SCIENCE BV},
	type = {Article},
	address = {PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS},
	abstract = {In this paper, we study the estimation of p-values for robust tests for the linear regression model. The asymptotic distribution of these tests has only been studied under the restrictive assumption of errors with known scale Or symmetric distribution. Since these robust tests are based on robust regression estimates, Efron{\textquoteright}s bootstrap (1979) presents a number of problems. In particular, it is computationally very expensive, and it is not resistant to outliers in the data. In other words, the tails of the bootstrap distribution estimates obtained by re-sampling the data may be severely affected by outliers. We show how to adapt the Robust Bootstrap (Ann. Statist 30 (2002) 556; Bootstrapping MM-estimators for linear regression with fixed designs, http://mathstat.carleton.ca/similar tomatias/pubs. html) to this problem. This method is very fast to compute, resistant to outliers in the data, and asymptotically correct under weak regularity assumptions. In this paper, we show that the Robust Bootstrap can be used to obtain asymptotically correct, computationally simple p-value estimates. A simulation study indicates that the tests whose p-values are estimated with the Robust Bootstrap have better finite sample significance levels than those obtained from the asymptotic theory based on the symmetry assumption. Although this paper is focussed on robust scores-type tests (in: Directions in Robust Statistics and Diagnostics, Part 1, Springer, New York), our approach can be applied to other robust tests (for example, Wald- and dispersion-type also discussed in Markatou et a]., 1991). (C) 2003 Elsevier B.V. All rights reserved.},
	keywords = {bootstrap, Robust inference, Robust regression, scores test, Wald test},
	issn = {0378-3758},
	doi = {10.1016/j.jspi.2003.09.033},
	author = {Salibian-Barrera, M}
}
@article {Bryan200444,
	title = {Problems in gene clustering based on gene expression data},
	journal = {Journal of Multivariate Analysis},
	volume = {90},
	number = {1},
	year = {2004},
	note = {Special Issue on Multivariate Methods in Genomic Data Analysis},
	pages = {44 - 66},
	abstract = {In this work, we assess the suitability of cluster analysis for the gene grouping problem confronted with microarray data. Gene clustering is the exercise of grouping genes based on attributes, which are generally the expression levels over a number of conditions or subpopulations. The hope is that similarity with respect to expression is often indicative of similarity with respect to much more fundamental and elusive qualities, such as function. By formally defining the true gene-specific attributes as parameters, such as expected expression across the conditions, we obtain a well-defined gene clustering parameter of interest, which greatly facilitates the statistical treatment of gene clustering. We point out that genome-wide collections of expression trajectories often lack natural clustering structure, prior to ad hoc gene filtering. The gene filters in common use induce a certain circularity to most gene cluster analyses: genes are points in the attribute space, a filter is applied to depopulate certain areas of the space, and then clusters are sought (and often found!) in the {\textquotedblleft}cleaned{\textquotedblright} attribute space. As a result, statistical investigations of cluster number and clustering strength are just as much a study of the stringency and nature of the filter as they are of any biological gene clusters. In the absence of natural clusters, gene clustering may still be a worthwhile exercise in data segmentation. In this context, partitions can be fruitfully encoded in adjacency matrices and the sampling distribution of such matrices can be studied with a variety of bootstrapping techniques.},
	keywords = {bootstrap},
	issn = {0047-259X},
	doi = {http://dx.doi.org/10.1016/j.jmva.2004.02.011},
	url = {http://www.sciencedirect.com/science/article/pii/S0047259X04000211},
	author = {Jenny Bryan}
}
@article { ISI:000173007800007,
	title = {CriSP: A tool for bump hunting},
	journal = {JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS},
	volume = {10},
	number = {4},
	year = {2001},
	month = {DEC},
	pages = {713-729},
	publisher = {AMER STATISTICAL ASSOC},
	type = {Article},
	address = {1429 DUKE ST, ALEXANDRIA, VA 22314 USA},
	abstract = {We propose a test of multimodality of regression functions and their derivatives. The test statistic is a critical smoothing parameter (CriSP), giving the minimum amount of smoothing necessary to force the regression function to satisfy the null hypothesis. The p values are computed via bootstrapping. Our idea is motivated by Silverman{\textquoteright}s test concerning the number of modes in the density function. Simulation studies indicate that the test works well, even when testing for bumps in the derivative. We apply CriSP to children{\textquoteright}s growth data, to study the number of spurts of growth.},
	keywords = {bootstrap, critical smoothing parameter, growth data, multimodality testing, Smoothing},
	issn = {1061-8600},
	doi = {10.1198/106186001317243412},
	author = {Harezlak, J and Heckman, NE}
}
@article { ISI:000088077700002,
	title = {Testing for monotonicity of a regression mean by calibrating for linear functions},
	journal = {ANNALS OF STATISTICS},
	volume = {28},
	number = {1},
	year = {2000},
	month = {FEB},
	pages = {20-39},
	publisher = {INST MATHEMATICAL STATISTICS},
	type = {Article},
	address = {IMS BUSINESS OFFICE-SUITE 7, 3401 INVESTMENT BLVD, HAYWARD, CA 94545 USA},
	abstract = {A new approach to testing. for monotonicity of a regression mean, not requiring computation of a curve estimator or a bandwidth, is suggested. It is based on the notion of {\textquoteleft}{\textquoteleft}running gradients{\textquoteright}{\textquoteright} over short, intervals, although from some viewpoints it may be regarded as an analogue for monotonicity testing of the dip/excess mass approach for testing modality hypotheses about densities. Like the latter methods, the new technique does not suffer difficulties caused by almost-Bat parts of the target function. In fact, it is calibrated so as to work well for flat response curves, and as a result it has relatively good power properties in boundary cases where the curve exhibits shoulders. Ln this respect, as well as in its construction, the {\textquoteleft}{\textquoteleft}running gradients{\textquoteright}{\textquoteright} approach differs from alternative techniques based on the notion of a critical bandwidth.},
	keywords = {bootstrap, calibration, curve estimation, Monte Carlo, response curve, running gradient},
	issn = {0090-5364},
	author = {Hall, P and Heckman, NE}
}
