Asymptotic theory for robust principal components (Q1088340)
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scientific article; zbMATH DE number 3990661
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotic theory for robust principal components |
scientific article; zbMATH DE number 3990661 |
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Asymptotic theory for robust principal components (English)
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1987
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The asymptotic distribution of the eigenvalues and eigenvectors of the robust scatter matrix, proposed by \textit{R. A. Maronna} [Ann. Stat. 4, 51- 67 (1976; Zbl 0322.62054)], is given when the observations are from an elliptical distribution. The elements of each characteristic vector are the coefficients of a robustified version of principal components. A definition for the asymptotic efficiency of the estimators is given and their influence curve is evaluated. The problem of maximizing the efficiency under a bound on the influence curve is solved.
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optimal estimators
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asymptotic distribution
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eigenvalues
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eigenvectors
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robust scatter matrix
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elliptical distribution
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robustified version of principal components
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influence curve
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