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- Mia Hubert, Peter Rousseeuw, Karlien Vanden Branden
- Technometrics
- 2005

In this paper we introduce a new method for robust principal component analysis. Classical PCA is based on the empirical covariance matrix of the data and hence it is highly sensitive to outlying observations. In the past, two robust approaches have been developed. The first is based on the eigenvectors of a robust scatter matrix such as the MCD or an… (More)

Since MATLAB is very popular in industry and academia, and is frequently used by chemometricians, statisticians, chemists, and engineers, we introduce a MATLAB library of robust statistical methods. Those methods were developed because their classical alternatives produce unreliable results when the data set contains outlying observations. Our toolbox… (More)

- Peter Rousseeuw, Mia Hubert
- Wiley Interdisc. Rew.: Data Mining and Knowledge…
- 2011

When analyzing data, outlying observations cause problems because they may strongly influence the result. Robust statistics aims at detecting the outliers by searching for the model fitted by the majority of the data. We present an overview of several robust methods and outlier detection tools. We discuss robust procedures for univariate, low-dimensional,… (More)

When applying a statistical method in practice it often occurs that some observations deviate from the usual assumptions. However, many classical methods are sensitive to outliers. The goal of robust statistics is to develop methods that are robust against the possibility that one or several unannounced outliers may occur anywhere in the data. These methods… (More)

- Mia Hubert, Katrien van Driessen
- Computational Statistics & Data Analysis
- 2004

The goal of discriminant analysis is to obtain rules that describe the separation between groups of observations. Moreover it allows to classify new observations into one of the known groups. In the classical approach discriminant rules are often based on the empirical mean and covariance matrix of the data, or of parts of the data. But because these… (More)

Deepest regression (DR) is a method for linear regression introduced by Rousseeuw and Hubert [20]. The DR method is defined as the fit with largest regression depth relative to the data. In this paper we show that DR is a robust method, with breakdown value that converges almost surely to 1/3 in any dimension. We construct an approximate algorithm for fast… (More)

- Peter Rousseeuw, Mia Hubert
- Discrete & Computational Geometry
- 1999

Peter J. Rousseeuw and Mia Hubert Revised version, 25 May 1998 Department of Mathematics and Computer Science, U.I.A., Universiteitsplein 1, B-2610 Antwerp, Belgium Peter.Rousseeuw@uia.ua.ac.be Abstract A collection of n hyperplanes in Rd forms a hyperplane arrangement. The depth of a point 2 Rd is the smallest number of hyperplanes crossed by any ray… (More)

- B. Vandewalle, J. Beirlant, Andreas Christmann, Mia Hubert
- Computational Statistics & Data Analysis
- 2007

In extreme value statistics, the extreme value index is a well-known parameter to measure the tail heaviness of a distribution. Pareto-type distributions, with strictly positive extreme value index (or tail index) are considered. The most prominent extreme value methods are constructed on efficient maximum likelihood estimators based on specific parametric… (More)

The views expressed in this paper are those of the authors and do not necessarily reflect the views of the National Bank of Belgium. Statement of purpose: The purpose of these working papers is to promote the circulation of research results (Research Series) and analytical studies (Documents Series) made within the National Bank of Belgium or presented by… (More)

Recent results about the robustness of kernel methods involve the analysis of influence functions. By definition the influence function is closely related to leave-one-out criteria. In statistical learning, the latter is often used to assess the generalization of a method. In statistics, the influence function is used in a similar way to analyze the… (More)