Multivariate statistics: a practical approach
Multivariate statistics: a practical approach
Goodness-of-fit analysis for multivariate normality based on generalized quantiles
Computational Statistics & Data Analysis
Influence function and efficiency of the minimum covariance determinant scatter matrix estimator
Journal of Multivariate Analysis
Outlier identification in high dimensions
Computational Statistics & Data Analysis
Assessing when a sample is mostly normal
Computational Statistics & Data Analysis
Error rates for multivariate outlier detection
Computational Statistics & Data Analysis
A Stahel-Donoho estimator based on huberized outlyingness
Computational Statistics & Data Analysis
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Robust distances are mainly used for the purpose of detecting multivariate outliers. The precise definition of cut-off values for formal outlier testing assumes that the ''good'' part of the data comes from a multivariate normal population. Robust distances also provide valuable information on the units not declared to be outliers and, under mild regularity conditions, they can be used to test the postulated hypothesis of multivariate normality of the uncontaminated data. This approach is not influenced by nasty outliers and thus provides a robust alternative to classical tests for multivariate normality relying on Mahalanobis distances. One major advantage of the suggested procedure is that it takes into account the effect induced by trimming of outliers in several ways. First, it is shown that stochastic trimming is an important ingredient for the purpose of obtaining a reliable estimate of the number of ''good'' observations. Second, trimming must be allowed for in the empirical distribution of the robust distances when comparing them to their nominal distribution. Finally, alternative trimming rules can be exploited by controlling alternative error rates, such as the False Discovery Rate. Numerical evidence based on simulated and real data shows that the proposed method performs well in a variety of situations of practical interest. It is thus a valuable companion to the existing outlier detection tools for the robust analysis of complex multivariate data structures.