Entropy for Random Partitions and Its Applications

Journal of Theoretical Probability

Volumn 11, Issue 2, 1998, Pages 417-433

  Shao, Yongzhao ^a   Jiménez, Raúl ^b  

^a Och Spine at New York Presbyterian Hospitals   (United States)

^b UNIVERSIDAD SIMÓN BOLÍVAR   (Venezuela)

Author keywords

Characterization of distributions; Entropy; Goodness of fit test; Kullback Liebler divergence; Martingale; Random partition; Spacings

Indexed keywords

EID: 0041633704     PISSN: 08949840     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022683822547     Document Type: Article

References (20)

1. de Acosta, A. (1994). Large deviations for vector-valued Lévy processes. Stoch. Proc. Appl. 51, 75-115.
2. Akaike, H. (1992). Information theory and an extension of the maximum likelihood principle. In Kotz, S., and Johnson, N. L. (Eds.), Breakthroughs in Statistics, Springer-Verlag, New York 1, 610-624.
3. Bartoszewicz, J. (1995). Bahadur and Hodges-Lehmann approximate efficiency of tests based on spacings. Statist. Probab. Lett. 23, 211-220.
4. Cheng, R. C. H., and Amin. N. A. K. (1983). Estimating parameters in continuous univariate distributions with a shifted origin. J. R. Statist. Soc. B. 45, 394-403.
5. Cheng, R. C. H., and Stephens, M. A. (1989). A goodness-of-fit test using Moran's statistic and estimated parameters. Biometrika 76, 385-392.
6. Czekala, F. (1993). Asymptotic distributions of statistics based on logarithm of spacings. Zastos. Mat. 21, 511-519.
7. Durrett, R. (1991). Probability: Theory and Examples. Wadsworth and Brooks/Cole Publishing Company, Pacific Grove, California.
8. Gebert, J. R., and Kale, B. K. (1969). Goodness of fit tests based on discriminatory information. Statist. Hefte. 3, 192-200.
9. Gzyl, H. (1995). The Method of Maximum Entropy. World Scientific Publishing.
10. Jiménez, R., and Palacios, J. L. (1997). Entropy of sample spacings and Kullback's information. Rebrape (Brazilian J. Probab. Statist.) 11, 1-10.
11. Kapur, J. N., and Kesavan, H. K. (1992). Entropy Optimization Principles with Applications. Academic Press, New York.
12. Kullback, S. (1959). Information Theory and Statistics. John Wiley and Sons, New York.
13. Petersen, K. (1984) Ergodic Theory. Cambridge University Press.
14. Ranneby, B. (1984). The maximum spacing method. An estimation method related to the maximum likelihood method. Scand. J. Statist. 11, 93-112.
15. Shao, Y., and Hahn, M. G. (1995). Limit Theorems for the Logarithm of Sample Spacings. Statist. Prob. Lett. 24, 121-132.
16. Shao, Y., and Hahn, M. G. (1996). On a distribution-free test of fit for continuous distribution functions. Scand. J. Statist. 23, 63-73.
17. Shao, Y., and Hahn, M. G. (1997). Strong consistency of the maximum product of spacings estimates with applications in nonparametrics and in estimation of unimodal densities. To appear in Ann. Inst. Statist. Math.
18. Shorack, G. R., and Wellner, J. A. (1986). Empirical Processes with Applications to Statistics. John Wiley, New York.
19. Slud, E. (1978). Entropy and maximal spacings for random partitions. Z. Wahr. verw. Geb. 41. 341-352.
20. Weiss, L. (1956). A certain class of tests of fit. Ann. Math. Statist. 27, 1165-1170.