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_ This paper presents a distribution free multivariate Kolmogorov-Smirnov goodness of fit test. The test uses an statistic which is built using Rosenblatt's transformation and an algorithm is developed to compute it in the bivariate case. An approximate test, that can be easily computed in any dimension, is also presented. The power of these multivariate tests is studied in a simulation study.

In this paper we consider the problem of building a linear prediction model when the number of candidate predictors is large and the data possibly contains anomalies that are difficult to visualize and clean. We aim at predicting the nonoutlying cases. Therefore, we need a method that is robust and scalable at the same time. We consider the stepwise algorithm LARS 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 dataset 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

We investigate the performance of robust estimates of multivariate location under nonstandard data contamination models such as componentwise outliers (i.e., contamination in each variable is independent from the other variables). This model brings up a possible new source of statistical error that we call "propagation of outliers." This source of error is unusual in the sense that it is generated by the data processing itself and takes place after the data has been collected. We define and derive the influence function of robust multivariate location estimates under flexible contamination models and use it to investigate the effect of propagation of outliers. Furthermore, we show that standard high-breakdown affine equivariant estimators propagate outliers and therefore show poor breakdown behavior under componentwise contamination when the dimension $d$ is high.Comment: Published in at http://dx.doi.org/10.1214/07-AOS588 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

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