Large sample behavior of entropy measures when parameters are estimated

Communications in Statistics - Theory and Methods

Volumn 26, Issue 2, 1997, Pages 483-501

  Pardo, L ^a   Salicru M ^b   Morales, D ^a   Menendez M L ^c  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b UNIVERSITY OF BARCELONA   (Spain)

^c UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

Author keywords

Asymptotic distribution; CAN estimators; Entropy measures; Random sampling; Stratified random sampling

Indexed keywords

NUMERICAL METHODS; OPTIMIZATION; PARAMETER ESTIMATION; RANDOM PROCESSES;

ASYMPTOTIC DISTRIBUTION; OPTIMUM ALLOCATION; RANDOM SAMPLING;

STATISTICS;

EID: 0031381122     PISSN: 03610926     EISSN: None     Source Type: Journal    
DOI: 10.1080/03610929708831929     Document Type: Article

References (22)

1. Arimoto, S. (1971). "Information-theoretical considerations on estimation problems". Information and Control, 19, 181-194.
2. Bernouilli (1713). "Ars conjectandi". Basileæ.
3. Dzhaparidze, K.O. and M.S. Nikulin (1974). "On a modification on the standard statistic of Pearson". Theory of Probability and its Applications, 19, 851-852.
4. Ferreri, C. (1980). "Hypoentropy and related heterogeneity divergence measures". Statistica, 40, 55-118.
5. Havrda, J. and F. Charvat (1967). "Concept of structural α-entropy". Kybernetika, 3, 30-35.
6. Kotz, S., Johnson, N.L. and D.W. Boyd (1967). "Series representation of distribution of quadratic forms in normal variables. I Central Case". A.M.S., 823-837.
7. Onicescu, O. (1966). "Energie Informationelle". C.R. Acad. Sci. París. Ser. A, 263, 841-842.
8. Pardo, L., Salicrú, M., Menéndez, M.L. and Morales, D. (1993). "The φ-divergence statistic in bivariate multinomial populations including stratification". Metrika, 40, 223-235.
9. Rao, J.N.K. and A.J. Scott (1981). "The analysis of categorical data from complex sample surveis: chi-squared tests for goodness of fit and independence in two-way tables". J. American Stat. Assoc., 76, 221-230.
10. Renyi, A. (1961). "On measures of entropy and information". Proc. 4th Berkeley Symp. Math. Statist. and Probl., 1, 547-561.
11. Salicrú, M., Menéndez, M.L., Morales, D. and Pardo, L. (1993). "Asymptotic distribution of (h,φ)-entropies". Communications in Statistics (Theory and Methods). Vol. 22 (7), 2015-2031.
12. Shannon, C.E. (1948). "A mathematical theory of communication". Bell. Syst. Tech. J., 27, 379-423.
13. Sharma, B.D. and Taneja, I.J. (1975). "Entropy of type (α,β) and other generalized measures in information theory". Ketrika, 22, 205-215.
14. Sharma, B.D. and P. Mittal (1977). "New non-additive measures of relative information". J. Comb. Inform. & Syst. Sci., 2, 122-133.
15. Taneja, I.J. (1975). A study of generalized measures in information theory. Ph. D. Thesis. University of Delhi.
16. Taneja, I.J. (1989). "On generalized information measures and their applications". Ad. Electronics and Electron Physics, 76, 327-413.
17. Vajda, I. and Vasek, K. (1985). "Majorization, concave entropies and comparison of experiments". Problems of Control and Information Theory, 14, 105-115.
18. Van der Lubbe, J.C.A. (1977). R-norm information and a general class of measures for certainty and information. M. Sc. Thesis, Delft University of Technology, Dept. E.E., (in dutch).
19. Van der Lubbe, J.C.A. (1981). A generalized probabilistic theory of the measurement of certainty and information. Ph. D. Thesis, Delft University of Technology, Dept. E.E.
20. Varma, R.S. (1966). "Generalizalions of Renyi's entropy of order α". J. Math. Sci., 1, 34-48.
21. Zografos, K., Ferentinos, K. and Papaioannou, T. (1990). "φ-Divergence statistics: sampling properties and multinomial goodness of fit and divergence tests". Communications in Statistics (Theory and Methods), 19(5), 1785-1802.
22. Zografos, K. (1992). "Asymptotic properties of φ-divergence statistic and its applications in contingency tables". Tech. Report # 185, Math. Dept., Univ. of Ioannina, to appear in the Int. J. of Mathematical and Statistical Sciences.