Maximum Lq-likelihood estimation

Annals of Statistics

Volumn 38, Issue 2, 2010, Pages 753-783

  Ferrari, Davide ^a   Yang, Yuhong ^b  

^a UNIVERSITY OF MODENA AND REGGIO EMILIA   (Italy)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Asymptotic efficiency; Exponential family; Maximum Lq likelihood estimation; Nonextensive entropy; Tail probability estimation

Indexed keywords

EID: 77649288406     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/09-AOS687     Document Type: Article

References (33)

1. ABE, S. (2003). Geometry of escort distributions. Phys. Rev. E 68 031101.
2. ACZÉL, J. D. and DARÓCZY, Z. (1975). On measures of information and their characterizations. Math. Sci. Eng. 115. Academic Press, New York-London.
3. AKAIKE, H. (1973). Information theory and an extension of the likelihood principle. In 2nd International Symposium of Information Theory 267-281. Akad. Kiadó, Budapest.
4. ALTUN, Y. and SMOLA, A. (2006). Unifying divergence minimization and statistical inference via convex duality. In Learning Theory. Lecture Notes in Computer Science 4005 139-153. Springer, Berlin.
5. BARRON, A., RISSANEN, J. and YU, B. (1998). The minimum description length principle in coding and modeling. IEEE Trans. Inform. Theory 44 2743-2760.
6. BASU, A. HARRIS, I. R., HJORT, N. L. and JONES, M. C. (1998). Robust and efficient estimation by minimising a density power divergence. Biometrika 85 549-559.
7. BECK, C. and SCHLÖGL, F. (1993). Thermodynamics of Chaotic Systems: An Introduction. Cambridge Univ. Press, Cambridge.
8. CHOI, E., HALL, P. and PRESNELL, B. (2000). Rendering parametric procedures more robust by empirically tilting the model. Biometrika 87 453-465.
9. COVER, T. M. and THOMAS, J. A. (2006). Elements of Information Theory.Wiley, New York.
10. DANIELS, H. E. (1997). Saddlepoint approximations in statistics (Pkg: P171-200). In Breakthroughs in Statistics (S. Kotz and N. L. Johnson, eds.) 3 177-200. Springer, New York.
11. FERGUSON, T. S. (1996). A Course in Large Sample Theory. Chapman & Hall, London.
12. FERRARI, D. and PATERLINI, S. (2007). The maximum Lq-likelihood method: An application to extreme quantile estimation in finance. Methodol. Comput. Appl. Probab. 11 3-19.
13. FIELD, C. and RONCHETTI, E. (1990). Small Sample Asymptotics. IMS, Hayward, CA.
14. GELL-MANN, M., ED. (2004). Nonextensive Entropy, Interdisciplinary Applications. Oxford Univ. Press, New York.
15. GOLDFARB, D. (1970). A family of variable-metric method derived by variational means. Math. Comp. 24 23-26.
16. HAVRDA, J. and CHARVÁT, F. (1967). Quantification method of classification processes: Concept of structural entropy. Kibernetika 3 30-35.
17. HUANG, J. Z., LIU, N., POURAHMADI, M. and LIU, L. (2006). Covariance matrix selection and estimation via penalised normal likelihood. Biometrika 93 85-98.
18. HUBER, P. J. (1981). Robust Statistics. Wiley, New York.
19. JAYNES, E. T. (1957). Information theory and statistical mechanics. Phys. Rev. 106 620.
20. JAYNES, E. T. (1957). Information theory and statistical mechanics II. Phys. Rev. 108 171.
21. KULLBACK, S. (1959). Information Theory and Statistics. Wiley, New York.
22. KULLBACK, S. and LEIBLER, R. A. (1951). On information and sufficiency. Ann. Math. Statistics 22 79-86.
23. LEHMANN, E. L. and CASELLA, G. (1998). Theory of Point Estimation. Springer, New York.
24. MAGNUS, J. R. and NEUDECKER, H. (1979). The commutation matrix: Some properties and applications. Ann. Statist. 7 381-394.
25. MCCULLOCH, C. E. (1982). Symmetric matrix derivatives with applications. J. Amer. Statist. Assoc. 77 679-682.
26. NAUDTS, J. (2004). Estimators, escort probabilities, and phi-exponential families in statistical physics. J. Inequal. Pure Appl. Math. 5 102.
27. RÉNYI, A. (1961). On measures of entropy and information. In Proc. 4th Berkeley Sympos. Math. Statist. and Prob. 1 547-1461 Univ. California Press, Berkeley.
28. SHANNON, C. E. (1948). A mathematical theory of communication. Bell System Tech. J. 27 379-423.
29. TSALLIS, C. (1988). Possible generalization of Boltzmann-Gibbs statistics. J. Statist. Phys. 52 479-487.
30. TSALLIS, C., MENDES, R. S. and PLASTINO, A. R. (1998). The role of constraints within generalized nonextensive statistics. Physica A: Statistical and Theoretical Physics 261 534-554.
31. VAN DER VAART, A. W. (1998). Asymptotic Statistics. Cambridge Univ. Press, Cambridge.
32. WANG, X., VAN EEDEN, C. and ZIDEK, J. V. (2004). Asymptotic properties of maximum weighted likelihood estimators. J. Statist. Plann. Inference 119 37-54.
33. WINDHAM, M. P. (1995). Robustifying model fitting. J. Roy. Statist. Soc. Ser. B 57 599-609.