Asymptotic expansion of S-estimators of location and covariance

Statistica Neerlandica

Volumn 51, Issue 2, 1997, Pages 220-237

  Lopuhaa H P ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Application of empirical process theory; Asymptotic normality of S estimators; Robust estimation of multivariate location and covariance

Indexed keywords

EID: 0031522603     PISSN: 00390402     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9574.00051     Document Type: Article

References (15)

1. DAVIES, P. L. (1987), Asymptotic behavior of S-estimates of multivariate location parameters and dispersion matrices, The Annals of Statistics 15, 1269-1292.
2. DAVIES, P. L. (1992), The asymptotics of Rousseeuw's minimum volume ellipsoid estimator, The Annals of Statistics 20, 1828-1843.
3. DEVLIN, S. J., R. GNANADESIKAN and J. R. KETTENRING (1981), Robust estimation of dispersion matrices and principal components, Journal of the American Statistical Association 76, 354-362.
4. DIEUDONNÉ, J. (1969), Foundations of modern analysis, Academic Press, New York and London.
5. EINMAHL, J. H. J. and D. M. MASON (1992), Generalized quantile processes, The Annals of Statistics 20, 1062-1078.
6. GRÜBEL, R. (1988), The length of the shorth, The Annals of Statistics 16, 619-628.
7. GRÜBEL, R. (1988), A minimal characterization of the covariance matrix, Metrika 35, 49-52.
8. LOPUHAÄ, H. P. (1989), On the relation between S-estimators and M-estimators of multivariate location and covariance, The Annals of Statistics 17, 1662-1683.
9. LOPUHAÄ, H. P. (1995), Asymptotics of robustly reweighted least squares estimators of location and covariance, in preparation.
10. LOPUHAÄ, H. P. and P. J. ROUSSEEUW (1991), Breakdown properties of affine equivariant estimators of multivariate location and covariance matrices, The Annals of Statistics 19, 229-248.
11. NOLAN, D. and D. POLLARD (1987), U-processes: Rates of convergence, The Annals of Statistics 15, 780-799.
12. POLLARD, D. (1984), Convergence of stochastic processes, Springer, New York.
13. ROUSSEEUW, P. J. (1985), Multivariate estimation with high breakdown point, in W. Grossmann, G. Pflug, I. Vincze and W. Wertz (eds), Mathematical statistics and applications, Vol. B, 283-297, Reidel, Dordrecht, The Netherlands.
14. ROUSSEEUW, P. J. and A. M. LEROY (1988), A robust scale estimator based on the shortest half, Statistica Neerlandica 42, 103-116.
15. TYLER, D. E. (1983), Robustness and efficiency properties of scatter matrices, Biometrika 70, 411-420.