High-Breakdown Robust Multivariate Methods
Mia Hubert, Peter J. Rousseeuw, and Stefan Van Aelst
Source: Statist. Sci. Volume 23, Number 1 (2008), 92-119.
Abstract
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 then allow to detect outlying observations by their residuals from a robust fit. We focus on high-breakdown methods, which can deal with a substantial fraction of outliers in the data. We give an overview of recent high-breakdown robust methods for multivariate settings such as covariance estimation, multiple and multivariate regression, discriminant analysis, principal components and multivariate calibration.
Keywords: Breakdown value; influence function; multivariate statistics; outliers; partial least squares; principal components; regression; robustness
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