Comprehensive definitions of breakdown points for independent and dependent observations

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 65, Issue 1, 2003, Pages 81-94

  Genton, Marc G ^a   Lucas, André ^b  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b VU UNIVERSITY AMSTERDAM   (Netherlands)

Author keywords

Bias curve; Linear regression; Non linear regression; Outliers; Statistical robustness; Time series

Indexed keywords

EID: 0141799716     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9868.00373     Document Type: Article

References (20)

1. Boente, G., Fraiman, R. and Yohai, V. J. (1987) Qualitative robustness for stochastic processes. Ann. Statist., 15, 1293-1312.
2. Donoho, D. L. and Huber, P. J. (1983) The notion of breakdown point. In A Festschrift for Erich L. Lehmann (eds P. J. Bickel, K. A. Doksum and J. L. Hodges, Jr), pp. 157-184. Belmont: Wadsworth.
3. Genton, M. G. (1998) Spatial breakdown point of variogram estimators. Math. Geol., 30, 853-871.
4. Hampel, F. R. (1971) A general qualitative definition of robustness. Ann. Math. Statist., 42, 1887-1896.
5. Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J. and Stahel, W. A. (1986) Robust Statistics: the Approach based on Influence Functions. New York: Wiley.
6. He, X. (1991) A local breakdown property of robust tests in linear regression. J. Multiv. Anal., 38, 294-305.
7. He, X. and Simpson, D. G. (1992) Robust direction estimation. Ann. Statist., 20, 351-369.
8. He, X. and Simpson, D. G. (1993) Lower bounds for contamination bias: globally minimax versus locally linear estimation. Ann. Statist., 21, 314-337.
9. He, X., Simpson, D. G. and Portnoy, S. L. (1990) Breakdown robustness of tests. J. Am. Statist. Ass., 85, 446-452.
10. Lucas, A. (1997) Asymptotic robustness of least median of squares for autoregressions with additive outliers. Communs Statist. Theory Meth., 26, 2363-2380.
11. Ma, Y. and Genton, M. G. (2000) Highly robust estimation of the autocovariance function. J. Time Ser. Anal., 21, 663-684.
12. Martin, R. D. (1980) Robust estimation of autoregressive models. In Directions in Time Series, pp. 228-262. Hayward: Institute of Mathematical Statistics.
13. Martin, R. D. and De Jong, J. (1977) Asymptotic properties of robust generalized M-estimates for the first-order autoregressive parameter. Technical Memorandum. Bell Laboratories, Murray Hill.
14. Rousseeuw, P. J. and Leroy, A. M. (1987) Robust Regression and Outlier Detection. New York: Wiley.
15. Sakata, S. and White, H. (1995) An alternative definition of finite sample breakdown point with applications to regression model estimators. J. Am. Statist. Ass., 90, 1099-1106.
16. Sakata, S. and White, H. (1998) High breakdown point conditional dispersion estimation with application to S&P 500 daily returns volatility. Econometrica, 66, 529-567.
17. Stefanski, L. A. (2000) Measurement error models. J. Am. Statist. Ass., 95, 1353-1358.
18. Stromberg, A. J. and Ruppert, D. (1992) Breakdown in nonlinear regression. J. Am. Statist. Ass., 87, 991-997.
19. Van Aelst, S. and Rousseeuw, P. J. (2000) Robustness of deepest regression. J. Multiv. Anal., 73, 82-106.
20. Zhang, J. and Li, G. (1998) Breakdown properties of location M-estimators. Ann. Statist., 26, 1170-1189.