Robust estimation for the multivariate linear model based on a τ-scale
| Autor: | Marta Garcia Ben, E. J. Martinez, Victor J. Yohai |
|---|---|
| Rok vydání: | 2006 |
| Předmět: |
Statistics and Probability
Numerical Analysis Mahalanobis distance Covariance matrix Linear model Multivariate regression Multivariate normal distribution Covariance Robust estimation Estimation of covariance matrices Scatter matrix Statistics Applied mathematics Statistics Probability and Uncertainty τ-estimates Elliptical distribution Mathematics |
| Zdroj: | Journal of Multivariate Analysis. 97:1600-1622 |
| ISSN: | 0047-259X |
| DOI: | 10.1016/j.jmva.2005.08.007 |
| Popis: | We introduce a class of robust estimates for multivariate linear models. The regression coefficients and the covariance matrix of the errors are estimated simultaneously by minimizing the determinant of the covariance matrix estimate, subject to a constraint on a robust scale of the Mahalanobis norms of the residuals. By choosing a τ-estimate as a robust scale, the resulting estimates combine good robustness properties and asymptotic efficiency under Gaussian errors. These estimates are asymptotically normal and in the case where the errors have an elliptical distribution, their asymptotic covariance matrix differs only by a scalar factor from the one corresponding to the maximum likelihood estimate. We derive the influence curve and prove that the breakdown point is close to 0.5. A Monte Carlo study shows that our estimates compare favorably with respect to S-estimates. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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