Estimating covariance and precision matrices along subspaces
| Autor: | Timo Klock, Željko Kereta |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
FOS: Computer and information sciences 62H12 62J10 62G08 dimension reduction Covariance matrix Machine Learning (stat.ML) Mathematics - Statistics Theory Statistics Theory (math.ST) ordinary least squares Matrix (mathematics) 62G08 Statistics - Machine Learning single-index model FOS: Mathematics Applied mathematics 62G05 Condition number Eigenvalues and eigenvectors Mathematics Dimensionality reduction Estimator Covariance finite sample bounds Linear subspace precision matrix 62J12 62H12 62J10 Statistics Probability and Uncertainty rate of convergence |
| Zdroj: | Electron. J. Statist. 15, no. 1 (2021), 554-588 |
| Popis: | We study the accuracy of estimating the covariance and the precision matrix of a $D$-variate sub-Gaussian distribution along a prescribed subspace or direction using the finite sample covariance. Our results show that the estimation accuracy depends almost exclusively on the components of the distribution that correspond to desired subspaces or directions. This is relevant and important for problems where the behavior of data along a lower-dimensional space is of specific interest, such as dimension reduction or structured regression problems. We also show that estimation of precision matrices is almost independent of the condition number of the covariance matrix. The presented applications include direction-sensitive eigenspace perturbation bounds, relative bounds for the smallest eigenvalue, and the estimation of the single-index model. For the latter, a new estimator, derived from the analysis, with strong theoretical guarantees and superior numerical performance is proposed. 25 pages, 9 figures |
| Databáze: | OpenAIRE |
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