Robust and efficient estimation by minimising a density power divergence

Biometrika

Volumn 85, Issue 3, 1998, Pages 549-559

  Basu, Ayanendranath ^a,c   Harris, Ian R ^b   Hjort, Nils L ^b   Jones, M C ^d  

^a INDIAN STATISTICAL INSTITUTE   (India)

^b NORTHERN ARIZONA UNIVERSITY   (United States)

^c UNIVERSITY OF OSLO   (Norway)

^d OPEN UNIVERSITY   (United Kingdom)

Author keywords

Af estimation; Asymptotic efficiency: Influence function; Maximum likelihood; Minimum distance estimation; Robustness

Indexed keywords

EID: 0001640740     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/85.3.549     Document Type: Article

References (23)

1. BASU, A. & LINDSAY, B. G. (1994). Minimum disparity estimation for continuous models: efficiency, distributions and robustness. Ann. Inst. Statist. Math. 48, 683-705.
2. BERAN, R. (1977). Minimum Hellinger distance estimates for parametric models. Ann. Statist. 5, 445-63.
3. BROWN, L. D. & H WANG, J. T. G. (1993). How to approximate a histogram by a normal density. Am. Statistician 47, 251-5.
4. CAO, R., CUEVAS, A. & FRAIMAN, R. (1995). Minimum distance density-based estimation. Comp. Statist. Data Anal 20, 611-31.
5. CRESSIE, N. & READ, T. R. C. (1984). Multinomial goodness-of-fit tests. J. R. Statist. Soc. B 46, 440-64.
6. FIELD, C. & SMITH, B. (1994). Robust estimation-a weighted maximum likelihood approach. Int. Statist. Rev. 62, 405-24.
7. HAMPEL, F. R., RONCHETTI, E. M., ROUSSEEUW, P. J. & STAHEL, W. A. (1986). Robust Statistics: The Approach Based on Influence Functions. New York: Wiley.
8. HERITIER, S. & RONCHETTI, E. (1994). Robust bounded-influence tests in general parametric models. J. Am. Statist. Assoc. 89, 897-904.
9. HJORT, N. L. (1994). Minimum L2 and robust Kullback-Leibler estimation. In Proceedings of the 12th Prague Conference on Information Theory, Statistical Decision Functions and Random Processes, Ed. P. Lachout and J. A. Visek, pp. 102-5. Prague: Academy of Sciences of the Czech Republic.
10. HUBER, P. J. (1981). Robust Statistics. New York: Wiley.
11. JONES, M. C. & HJORT, N. L. (1994). Comment on Brown & Hwang (1993). Am. Statistician 48, 353-4.
12. KULLBACK, S. & LEIBLER, R. A. (1951). On information and sufficiency. Ann. Math. Statist. 22, 79-86.
13. LINDSAY, B. G. (1994). Efficiency versus robustness: the case for minimum Hellinger distance and related methods. Ann. Statist. 22, 1081-114.
14. MOORE, D. S. & MCCABE, G. P. (1993). Introduction to the Practice of Statistics, 2nd ed. New York: W.H. Freeman.
15. NEYMAN, J. (1949). Contribution to the theory of/2 tests. In Proceedings of the First Berkeley Symposium in Mathematics and Statistics, pp. 239-73. Berkeley, CA: University of California Press.
16. RAO, C. R. (1963). Criteria of estimation in large samples. Sankhyâ A 25, 189-206.
17. RAO, C. R. (1965). Linear Statistical Inference and its Applications. New York: Wiley.
18. RONCHETTI, E. (1997). Robustness aspects of model choice. Statist. Sinica 7, 327-38.
19. SIMPSON, D. G. (1987). Minimum Hellinger distance estimation for the analysis of count data. J. Am. Statist. Assoc. 82, 802-7.
20. TAMURA, R. N. & Boos, D. D. (1986). Minimum Hellinger distance estimation for multivariate location and covariance. J. Am. Statist. Assoc. 81, 223-9.
21. TERRELL, G. R. (1993). Spline density estimates. In Proc. Statist. Comp. Sect., pp. 255-60. Washington, DC: Am. Statist. Assoc.
22. VICTORIA-FESER, M. P. & RONCHETTI, E. (1997). Robust estimation for grouped data. J. Am. Statist. Assoc. 92, 333-40.
23. WINDHAM, M. P. (1995). Robustifying model fitting. J. R. Statist. Soc. B 57, 599-609.