On Efficient Estimation in Continuous Models Based on Finitely Quantized Observations

References

• Beirlant , J. , Györfi , L. , Lugosi , G. ( 1994 ). On the asymptoic normality of the L 1- and L 2-errors in histogram density estimation . Canad. J. Statist. 22 : 309 – 318 . [CSA]
   Web of Science ®Google Scholar
• Bickel , P. J. ( 1982 ). On adaptive estimation . Ann. Statis. 10 : 647 – 671 . [CSA]
   Web of Science ®Google Scholar
• Cox , C. ( 1984 ). An elementary introduction to maximum likelihood estimation for multinomial models: Birch's theorem and delta method . Amer. Statist. 38 : 283 – 287 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Cressie , N. A. C. , Read , R. C. ( 1984 ). Multinomial goodness of fit tests . J. Royal Statist. Soc., Ser. B 46 : 440 – 464 . [CSA]
   Google Scholar
• Csiszár , I. ( 1963 ). Eine informationstheoretische ungleichung und ihre anwendung auf den beweis der ergodizität von markoffschen ketten . Publ. Math. Inst. Hung. Acad. Sci., Ser. A 8 : 85 – 108 . [CSA]
   Google Scholar
• Csiszár , I. ( 1967 ). Information type measures of difference of probability distributions and indirect observations . Studia Sci. Math. Hung. 2 : 299 – 318 . [CSA]
   Google Scholar
• Drost , D. C. ( 1989 ). Generalized chi-square goodness-of-fit tests for location-scale models when the number of classes tends to infinity . Ann. Statist. 17 : 1285 – 1300 . [CSA]
   Web of Science ®Google Scholar
• Dzhaparidze , K. O. , Nikulin , M. S. ( 1974 ). On a modification of the standard statistics Pearson . Theory Probab. Appl. 19 : 851 – 851 . [CSA] [CROSSREF]
   Google Scholar
• Fleming , W. ( 1977 ). Functions of Several Variables. , 2nd ed. New York : Springer-Verlag .
   Google Scholar
• Ghurye , S. G. , Johnson , B. R. ( 1981 ). Discrete approximations to the information integral . Canad. J. Statist. 9 : 27 – 37 . [CSA] [CROSSREF]
   Google Scholar
• Györfi , L. , Vajda , I. ( 2002 ). Asymptotic distributions for goodness-of-fit statistics in a sequence of multinomial models . Statist. Probab. Lett. 56 : 57 – 67 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Liese , F. , Vajda , I. ( 1987 ). Convex Statistical Distances . Leipzig : Teubner .
   Google Scholar
• Lindsay , B. G. ( 1994 ). Efficiency versus robustness: the case for minimum Hellinger distance and other methods . Ann. Statist. 22 : 1081 – 1114 . [CSA]
   Web of Science ®Google Scholar
• Menéndez , M. L. , Morales , D. , Pardo , L. , Vajda , I. ( 1998 ). Two approaches to grouping of data and related disparity statistics . Commun. Statist. Theory Meth. 27 : 609 – 633 . [CSA]
   Web of Science ®Google Scholar
• Menéndez , M. L. , Morales , D. , Pardo , L. , Vajda , I. ( 2001 ). Minimum divergence estimators based on grouped data . Ann. Inst. Statist. Math. 53 : 277 – 288 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Moore , D. S. , Spruil , M. C. ( 1975 ). Unified large-sample theory of general chi-squared statistics for tests of fit . Ann. Statist. 3 : 599 – 616 . [CSA]
   Web of Science ®Google Scholar
• Pardo , L. ( 2006 ). Statistical Inference Based on Divergence Measures . Statistics: Texbooks and Monographs . Chapman & Hall/CRC : New York .
   Google Scholar
• Rao , C. R. ( 1973 ). Linear Statistical Inference and Its Applications. , 2nd ed. New York : John Wiley .
   Google Scholar
• Rao , K. C. , Robson , D. S. ( 1974 ). A chi-square statistic for goodness-of-fit tests within the exponential family . Commun. Statist. Theory Meth. 3 : 1139 – 1153 . [CSA]
   Google Scholar
• Read , R. C. , Cressie , N. A. C. (1988). Goodness-of-Fit Statistics for Discrete Multivariate Data . New York : Springer Verlag.
   Google Scholar
• Ryu , K. ( 1993 ). Monotonicity of the Fisher information and Kullback–Leibler divergence measure . Econ. Lett. 42 : 121 – 128 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Serfling , R. J. ( 1980 ). Approximation Theorems of Mathematical Statistics . New York : John Wiley .
   Google Scholar
• Tsairidis , Ch. , Zografos , K. , Ferentinos , K. ( 1997 ). Fisher's information matrix and divergence for finite and optimal partitions of the sample space . Commun. Statist. Theory Meth. 26 : 2271 – 2289 . [CSA]
   Web of Science ®Google Scholar
• Vajda , I. ( 1972 ). On the f-divergence and singularity of probability measures . Period. Math. Hung. 6 : 317 – 324 . [CSA]
   Google Scholar
• Vajda , I. ( 1973 ). χα-divergence and generalized Fisher information . In: Transactions of the Sixth Prague Conference on Information Theory, Statistical Decision Functions and Random Processes . Prague : Academia , pp. 873 – 886 .
   Google Scholar
• Vajda , I. ( 1984a ). Minimum divergence principle in statistical estimation . Statist. Decis. 1 ( Supp. ): 239 – 261 . [CSA]
   Google Scholar
• Vajda , I. ( 1984b ). Motivation, existence and equivariance of D-estimators . Kybernetika 20 : 189 – 208 . [CSA]
   Web of Science ®Google Scholar
• Vajda , I. ( 1984c ). Consistency of D-estimators . Kybernetika 20 : 283 – 303 . [CSA]
   Web of Science ®Google Scholar
• Vajda , I. ( 1984d ). Asymptotic efficiency and robustness of D-estimators . Kybernetika 20 : 358 – 375 . [CSA]
   Web of Science ®Google Scholar
• Vajda , I. ( 1989 ). Theory of Statistical Inference and Information . Boston : Kluwer .
   Google Scholar
• Vajda , I. ( 2002 ). On convergence of information contained in quantized observations . Trans. IEEE Inform. Theory 48 : 2163 – 2172 . [CSA] [CROSSREF]
   Google Scholar
• Vos , P. V. ( 1992 ). Minimum f-divergence estimators and quasi-likelihood functions . Ann. Inst. Statist. Math. 44 : 261 – 279 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Watson , G. S. ( 1959 ). Some recent results in chi-square goodness-of-fit tests . Biometrics 15 : 440 – 468 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Zografos , K. , Ferentinos , K. , Papaioannou , T. ( 1986 ). Discrete approximations to the Csiszár, Rényi and Fisher measures of information . Canad. J. Statist. 14 : 355 – 366 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar