A generalized spatial sign covariance matrix
| Autor: | Peter J. Rousseeuw, Jakob Raymaekers |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability Numerical Analysis Covariance matrix Computation Mathematical analysis 020206 networking & telecommunications 02 engineering and technology 01 natural sciences Methodology (stat.ME) 010104 statistics & probability Data point Scatter matrix Robustness (computer science) Principal component analysis Outlier 0202 electrical engineering electronic engineering information engineering 0101 mathematics Statistics Probability and Uncertainty Statistics - Methodology Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Journal of Multivariate Analysis, 171, 94-111. Academic Press Inc. |
| ISSN: | 0047-259X |
| DOI: | 10.1016/j.jmva.2018.11.010 |
| Popis: | © 2018 The Authors The well-known spatial sign covariance matrix (SSCM) carries out a radial transform which moves all data points to a sphere, followed by computing the classical covariance matrix of the transformed data. Its popularity stems from its robustness to outliers, fast computation, and applications to correlation and principal component analysis. In this paper we study more general radial functions. It is shown that the eigenvectors of the generalized SSCM are still consistent and the ranks of the eigenvalues are preserved. The influence function of the resulting scatter matrix is derived, and it is shown that its asymptotic breakdown value is as high as that of the original SSCM. A simulation study indicates that the best results are obtained when the inner half of the data points are not transformed and points lying far away are moved to the center. ispartof: JOURNAL OF MULTIVARIATE ANALYSIS vol:171 pages:94-111 status: published |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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