A cautionary note on robust covariance plug-in methods
By Klaus Nordhausen, David E. Tyler. 2014
51 citations recorded by the source corpus.
The sample covariance matrix, which is well known to be highly nonrobust, plays a central role in many classical multivariate statistical methods. A popular way of making such multivariate methods more robust is to replace the sample covariance matrix with some robust scatter matrix. The aim of this paper is to point out that multivariate methods often require that certain properties of the covariance matrix hold also for the robust scatter matrix in order for the corresponding robust plug-in method to be a valid approach, but that not all scatter matrices possess the desired properties. Plug-in methods for independent components analysis, observational regression and graphical modelling are considered in more detail. For each case, it is shown that replacing the sample covariance matrix with a symmetrized robust scatter matrix yields a valid robust multivariate procedure.
Subfields: Analytical Chemistry, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/c2bb895ca3953e95ba1677a16197600d7d1db12c
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In Statistics and Probability
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Citations in the corpus
- Choosing Among Notions of Multivariate Depth Statistics (2020, background): “However, note that plugging-in a robust scatter estimator in place of the usual covariance matrix can influence the stochastic properties of the depth statistic; see Nordhausen and Tyler (2015).”