• 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)
• 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 estima-tors based on specific parametric(More)
• 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)
• 1999
A collection of n hyperplanes in R d forms a hyperplane arrangement. The depth of a point 2 R d is the smallest number of hyperplanes crossed by any ray emanating from. For d = 2 we prove that there always exists a point with depth at least dn=3e. For higher dimensions we conjecture that the maximal depth is at least dn=(d + 1)e. For arrangements in general(More)
• 2004
MOTIVATION Principal components analysis (PCA) is a very popular dimension reduction technique that is widely used as a first step in the analysis of high-dimensional microarray data. However, the classical approach that is based on the mean and the sample covariance matrix of the data is very sensitive to outliers. Also, classification methods based on(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(More)
• 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)
• 2006
The kurtosis coefficient is often regarded as a measure of the tail heaviness of a distribution relative to that of the normal distribution. However, it also measures the peakedness of a distribution, hence there is no agreement on what kurtosis really estimates. Another disadvantage of the kurtosis is that its interpretation and consequently its use is(More)