Abstract
This chapter is the most important chapter for outlier robust statistics and covers robust estimators of multivariate location and dispersion. The practical, highly outlier resistant, \(\sqrt{n}\) consistent FCH, RFCH, and RMVN estimators of \((\varvec{\mu }, c \varvec{\varSigma })\) are developed along with proofs. The RFCH and RMVN estimators are reweighted versions of the FCH estimator. It is shown why competing “robust estimators” fail to work, are impractical, or are not yet backed by theory. The RMVN and RFCH sets are defined and will be used to create practical robust methods of principal component analysis, canonical correlation analysis, discriminant analysis, factor analysis, and multivariate linear regression in the following chapters.
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Olive, D.J. (2017). MLD Estimators. In: Robust Multivariate Analysis. Springer, Cham. https://doi.org/10.1007/978-3-319-68253-2_4
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DOI: https://doi.org/10.1007/978-3-319-68253-2_4
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-68251-8
Online ISBN: 978-3-319-68253-2
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