On efficiency of estimation and testing with data quantized to fixed number of cells

Metrika

Volumn 57, Issue 1, 2003, Pages 1-27

  Mayoral, A M ^a   Morales, D ^a   Morales, J ^a   Vajda, I ^b  

^a MIGUEL HERNÁNDEZ UNIVERSITY   (Spain)

^b INSTITUTE OF INFORMATION THEORY AND AUTOMATION   (Czech Republic)

Author keywords

Convergence of Fisher information; Efficient estimation; Efficient testing; Fisher information in quantized models; Optimal quantization; Quantization

Indexed keywords

EID: 17444430770     PISSN: 00261335     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001840100178     Document Type: Article

References (30)

1. Basu A, Sarkar S (1994a) Minimum disparity estimation in the errors-invariables model. Statistics and Probability Letters 20:69-73
2. Basu A, Sarkar S (1994b) The trade-off between robustness and efficiency and the effect of model smoothing. Journal of Statistics, Computation and Simulation 50:173-185
3. Birch MW (1964) A new proof of the Pearson-Fisher theorem. Annals of Mathematical Statistics 35:817-824
4. Brent RP (1973) Algorithms for minimization without derivatives. Prentice Hall
5. Brown BW, Lovato J, Russell K (1994) Library of routines for cumulative distribution functions, inverses, and other parameters, http://www.stat.unipg. it/stat/dcdflib/
6. Cheng SW (1975) A unified approach to choosing optimum quantiles for the ABLEs. Journal of the American Statistical Association 70:155-159
7. Csiszár I (1963) Eine informationstheoretische Ungleichung und ihre anwendung auf den beweis der ergodizität on markoffschen ketten. Publications of the Mathematical Institute of the Hungarian Academy of Sciences 8, Ser. A, 84-108.
8. Csiszár I (1967) Information-type measured of difference of probability distributions and indirect observations. Studia Scientiarium Mathematica Hungarica 2:299-318
9. Ghurye SG, Johnson BR (1981) Discrete approximations to the information integral. The Canadian Journal of Statistics 9:27-37
10. Inglot T, Jurlewicz T, Ledwina T (1991) Asymptotics for multinomial goodness of fit tests for simple hypotheses. Theory of Probability and Applications 35:771-777
11. Liese F, Vajda I (1987) Convex statistical distances. Leipzig, Teubner
12. Lindsay BG (1994) Efficiency versus robustness: The case of minimum Hellinger distance and other methods. Annals of Statistics 22:1081-1114
13. Menéndez ML, Morales D, Pardo L, Vajda I (1998) Two approaches to grouping of data and related disparity statistics. Communications in Statistics-Theory and Methods 27:609-633
14. Menéndez ML, Morales D, Pardo L, Vajda I (2001a) Minimum disparity estimators for discrete and continuous models. Applications of Mathematics (in print)
15. Menéndez ML, Morales D, Pardo L, Vajda I (2001b) Approximations to powers of φ-disparity goodness of fit tests. Communications in Statistics-Theory and Methods 30:105-134
16. Millar PW (1984) A general approach to the optimality of minimum distance estimators. Transactions of the American Mathematical Society 286:377-418
17. Morales D, Pardo L, Vajda I (1995) Asymptotic divergence of estimates of discrete distributions. Journal of Statistical Planning and Inference 48:347-369
18. Park Ch, Basu A, Basu S (1995) Robust minimum distance inference based on combined distances. Communications in Statistics - Simulation and Computation 24:653-673
19. Pötzelberger K, Felsenstein K (1993) On the Fisher information of discretized data. Journal of Statistics, Computation and Simulation 46:125-144
20. Powell MJD (1964) An efficient method for finding the minimum of a function of several variables without calculating derivatives. Computation Journal 7:155-162
21. Rao CR (1961) Asymptotic efficiency and limiting information. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1:531-545. Berkeley, CA, Berkeley University Press
22. Read RC, Cressie NAC (1988) Goodness-of-fit statistics for discrete multivariate data. New York, Springer Verlag
23. Serfling RJ (1980) Approximation theorems of mathematical statistics. Wiley, New York
24. Tsaridis Ch, Zografos K, Ferentinos K (1997) Fisher's information matrix and divergence for finite and optimal partitions of the sample space. Communications in Statistics-Theory and Methods 26:2271-2289
25. α-divergence and generalized Fisher information. Trans. of the Sixth Prague Conference on Information Theory, Statistical Decision Functions and Random Processes. Prague, Academia, pp. 223-234
26. Vajda I (1989) Theory of statistical inference and information. Boston, Kluwer Academic Publishers
27. Vajda I (1995) Conditions equivalent to consistency of approximate MLE's for stochastic processes. Stochastic Processes and their Applications 56:35-56
28. Vajda I (2001) On the convergence of information contained in quantized observations. IEEE Transactions on Information Theory (in print)
29. Vajda I, Janžura M (1997) On asymptotically optimal estimates for general observations. Stochastic Processes and their Applications 72:27-45
30. Zografos K, Ferentinos K, Papaioannou T (1986) Discrete approximations to the Csiszár, Rényi, and Fisher measures of information. The Canadian Journal of Statistics 14:355-366