Generalized measures of divergence in survival analysis and reliability

Journal of Applied Probability

Volumn 47, Issue 1, 2010, Pages 216-234

  Vonta, Filia ^a   Karagrigoriou, Alex ^b  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

^b UNIVERSITY OF CYPRUS   (Cyprus)

Author keywords

Cox model; Csisz r's family of measures; Divergence measure; Frailty model; Proportional reverse hazards model

Indexed keywords

EID: 80053924730     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0021900200006501     Document Type: Article

References (23)

1. ALI, S. M. AND SILVEY, S. D. (1966). A general class of coefficients of divergence of one distribution from another. J. R. Statist. Soc. B 28, 131-142.
2. BALAKRISHNAN, V. AND SANGHVI, L. D. (1968). Distance between populations on the basis of attribute. Biometrics 24, 859-865.
3. 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.
4. COX, D. R. (1972). Regression models and life tables. J. R. Statist. Soc. B 34, 187-202.
5. CRESSIE, N. AND READ, T. R. C. (1984). Multinomial goodness-of-fit tests. J. R. Statist. Soc. B 46, 440-464.
6. CSISZÁR, I. (1963). Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizitat on Markhoffschen Ketten. Magyar Tud. Akad. Mat. Kutató Int. Közl. 8, 84-108.
7. DI CRESCENZO, A. (2000). Some results on the proportional reversed hazards model. Statist. Prob. Lett. 50, 313-321.
8. DI CRESCENZO, A. AND LONGOBARDI, M. (2004). A measure of discrimination between past lifetime distributions. Statist. Prob. Lett., 67, 173-182.
9. EBRAHIMI, N. AND KIRMANI, S. N. U. A. (1996a). A characterization of the proportional hazards model through a measure of discrimination between two residual life distributions. Biometrika 83, 233-235.
10. EBRAHIMI, N. AND KIRMANI, S. N. U. A. (1996b). A measure of discrimination between two residual life-time distributions and its applications. Ann. Inst. Statist. Math. 48, 257-265.
11. GUPTA, R. C., GUPTA, P. L. AND GUPTA, R. D. (1998). Modeling failure time data by Lehmann alternatives. Commun. Statist. Theory Meth. 27, 887-904.
12. KAGAN, A. M. (1963). On the theory of Fisher's amount of information. Soviet Math. Dokl. 4, 991-993.
13. KIRMANI, S. N. U. A. AND GUPTA, R. C. (2001). On the proportional odds model in survival analysis. Ann. Inst. Statist. Math. 53, 203-216.
14. KOLMOGOROV, A. N. (1933). Sulla determinazione empirica di una legge di distribuzione. Giornale dell'Instituto Italiano degli Attuari 4, 83-91.
15. KULLBACK, S. AND LEIBLER, R. A. (1951). On information and sufficiency. Ann. Math. Statist. 22, 79-86.
16. LÉVY, P. (1925). Calcul des Probabilites. Gauthiers-Villars, Paris.
17. MAHALANOBIS, P. C. (1936). On the generalized distance in statistics. Proc. Nat. Acad. Sci. India 2, 49-55.
18. MATTHEOU, K., LEE, S. AND KARAGRIGORIOU, A. (2009). A model selection criterion based on the BHHJ measure of divergence. J. Statist. Planning Infer. 139, 228-235.
19. MATUSITA, K. (1967). On the notion of affinity of several distributions and some of its applications. Ann. Inst. Statist. Math. 19, 181-192.
20. PARDO, L. (2006). Statistical Inference Based on Divergence Measures. Chapman and Hall/CRC, Boca Raton, FL.
21. PEARSON, K. (1900). On the criterion that a given system of deviation from the probable in the case of a correlated system of variables in such that it can be reasonably supposed to have arisen from random sampling. Phil. Mag. 50, 157-172.
22. SHAKED, M. AND SHANTHIKUMAR, J. G. (1994). Stochastic Orders and Their Applications. Academic Press, Boston, MA.
23. VONTA, F. (1996). Efficient estimation in a non-proportional hazards model in survival analysis. Scand. J. Statist. 23, 49-61.