DOI: 10.1214/aos/1015956714. On the uniqueness of S-functionals and M-functionals under nonelliptical distributions

On the uniqueness of S-functionals and M-functionals under nonelliptical distributions

10.1214/aos/1015956714

Crossref journal-article

Institute of Mathematical Statistics

The Annals of Statistics (108)

Bibliography

Tatsuoka, K. S., & Tyler, D. E. (2000). On the uniqueness of S-functionals and M-functionals under nonelliptical distributions. The Annals of Statistics, 28(4).

Authors 2

Kay S. Tatsuoka (first)
David E. Tyler (additional)

References 18 Referenced 121

Anderson, T. W. (1955). The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities. Proc.Amer.Math.Soc.6 170-176. (10.2307/2032333)
Bonneson, T. and Fenchel, W. (1987). Theory of Convex Bodies. BCS Assoc., Moscow, Idaho.
Davies, P. L. (1987). Asymptotic behavior of S-estimates of multivariate location parameters and dispersion matrices. Ann.Statist.15 1269-1292. (10.1214/aos/1176350505)
Davies, P. L. (1992). The asymptotics of Rousseeuw's minimum volume ellipsoid estimator. Ann. Statist. 20 1828-1843. (10.1214/aos/1176348891)
Davies, P. L. (1993). Aspects of robust linear regression. Ann.Statist.21 1843-1899. (10.1214/aos/1176349401)
Kent, J. and Tyler, D. E. (1996). Constrained M-estimation for multivariate location and scatter. Ann.Statist.24 1346-1370. (10.1214/aos/1032526973)
Kent, J. and Tyler, D. E. (1997). Regularity and uniqueness for M-estimates of scale. Technical report, Univ. Leeds, England.
Lopuha¨a, H. (1989). On the relation between S-estimators and M-estimators of multivariate location and covariance. Ann.Statist.17 1662-1683. (10.1214/aos/1176347386)
Lopuha¨a, H. (1992). Highly efficient estimators of multivariate location with high breakdown point. Ann.Statist.20 398-413. (10.1214/aos/1176348529)
Mendes, B. and Tyler, D. E. (1996). Constrained M-estimation for regression. Robust Statistics, Data Analysis, and Computer Intensive Methods.Lecture Notes in Statist.109 229-320. Springer, New York. (10.1007/978-1-4612-2380-1_20)
Nolan, D. (1991). The excess-mass ellipsoid. J.Multivariate Anal.39 348-371. (10.1016/0047-259X(91)90106-C)
Rousseeuw, P. J. (1986). Multivariate estimation with high breakdown point. In Mathematical Statistics and Applications (W. Grossman, G. Pflug, I. Vincze and W. Wertz, eds.) 283- 297. Reidel, Dordrecht. (10.1007/978-94-009-5438-0_20)
Rousseeuw, P. J. and Yohai, V. (1984). Robust regression by means of S-estimators. Robust and Nonlinear Time Series Analysis.Lecture Notes in Statist.26 256-272. Springer, New York. (10.1007/978-1-4615-7821-5_15)
Marshall, A. W. and Olkin, I. (1979). Inequalities: Theory of Majorization and Its Applications. Academic Press, New York.
Rousseeuw, P. J. and Leroy, A. M. (1987). Robust Regression and Outlier Detection. Wiley, New York. (10.1002/0471725382)
Martin, R. D., Yohai, V. J. and Zamar, R. H. (1989). Min-max bias robust regression. Ann. Statist. 17 1608-1630. (10.1214/aos/1176347384)
Yohai, V. J. (1987). High breakdown point and high efficiency robust estimates for regression. Ann.Statist.15 642-656. (10.1214/aos/1176350366)
Tyler, D. E. (1983). Robustness and efficiency properties of scatter matrices. Biometrika 70 411-420. (10.1093/biomet/70.2.411)

Dates

Type	When
Created	22 years, 10 months ago (Oct. 11, 2002, 4:16 p.m.)
Deposited	4 years, 3 months ago (May 9, 2021, 12:47 a.m.)
Indexed	1 month, 4 weeks ago (July 1, 2025, 1:24 p.m.)
Issued	25 years ago (Aug. 1, 2000)
Published	25 years ago (Aug. 1, 2000)
Published Print	25 years ago (Aug. 1, 2000)

Funders 0

None

BibTeX

@article{Tatsuoka_2000, title={On the uniqueness of S-functionals and M-functionals under nonelliptical distributions}, volume={28}, ISSN={0090-5364}, url={http://dx.doi.org/10.1214/aos/1015956714}, DOI={10.1214/aos/1015956714}, number={4}, journal={The Annals of Statistics}, publisher={Institute of Mathematical Statistics}, author={Tatsuoka, Kay S. and Tyler, David E.}, year={2000}, month=aug }

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