6533b7d8fe1ef96bd126a171
RESEARCH PRODUCT
Robustifying principal component analysis with spatial sign vectors
Sara TaskinenSara TaskinenHannu OjaInge Kochsubject
Statistics and ProbabilityMathematical optimizationEstimation of covariance matricesMatérn covariance functionCovariance functionCovariance matrixLaw of total covarianceApplied mathematicsRational quadratic covariance functionCovariance intersectionStatistics Probability and UncertaintyCovarianceMathematicsdescription
Abstract In this paper, we apply orthogonally equivariant spatial sign covariance matrices as well as their affine equivariant counterparts in principal component analysis. The influence functions and asymptotic covariance matrices of eigenvectors based on robust covariance estimators are derived in order to compare the robustness and efficiency properties. We show in particular that the estimators that use pairwise differences of the observed data have very good efficiency properties, providing practical robust alternatives to classical sample covariance matrix based methods.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-04-01 | Statistics & Probability Letters |