Publication:
On Burbea-Rao divergence based goodness-of-fit tests for multinomial models

Loading...
Thumbnail Image
Full text at PDC
Publication Date
1999-04
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Academic Press
Citations
Google Scholar
Research Projects
Organizational Units
Journal Issue
Abstract
This paper investigates a new family of statistics based on Burbea-Rao divergence for testing goodness-of-fit. Under the simple and composite null hypotheses the asymptotic distribution of these tests is shown to be chi-squared. For composite hypothesis, the unspecified parameters are estimated by maximum likelihood as well as minimum Burbea-Rao divergence.
Description
This work was supported by Grant DGES PB96-0635 and PR156/97-7159.
Unesco subjects
Keywords
Citation
M.S. Ali, D. Silvey, A general class of coefficients of divergence of one distribution from another. J. Roy. Statist. Soc. Ser. B, 28 (1966), pp. 131–140 T. Bednarski, T. Ledwina, A note on a biasedness of tests of fit. Math. Oper. Statist. Ser. Statist., 9 (1978), pp. 191–193 M.W. Birch, A new proof of the Pearson–Fisher theorem. Ann. of Math. Statist., 35 (1964), pp. 817–824 J. Burbea, C.R. Rao, On the convexity of some divergence measures based on Entropy functions. IEEE Trans. Inform. Theory, 28 (1982), pp. 489–495 J. Burbea, C.R. Rao, On the convexity of higher order Jensen differences based on entropy function. IEEE Trans. Inform. Theory, 28 (1982), pp. 961–963 J. Burbea, J-divergences and related topics, Encyclopedia Statist. Sci. 44 (1983), 290-296. W.G. Cochran, The Theχ2 test of goodness of fit, Ann. of Math. Statist., 23 (1952), pp. 315–345 A. Cohen, H.B. Sackrowitz, Unbiasedness of the chi-square, likelihood ratio, and other goodness of fit tests for the equal cell case. Ann. Statist., 3 (1975), pp. 959–964 N.Cressie,T.R.C. Read, Multinomial goodness of fit test. J. Roy. Statist. Soc. Ser. B, 46 (1984), pp. 440–464 I. Csiszár, Eine Informationtheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizität von Markhoffschen Ketten. Publ. Math. Inst. Hung. Acad. Sci. Ser. A, 8 (1963), pp. 85–108 J.J. Dik, M.C.M. Gunst, The distribution of general quadratic forms in normal variables. Statist. Neerlandica, 39 (1985), pp. 14–26 A.R. Eckler, A survey of coverage problems associated with point and area targets. Technometrics, 11 (1969), pp. 561–589 R.A. Fisher, The conditions under whichχ2. J. Roy. Statist. Soc., 87 (1924), pp. 442–450 C. Gini, Variabilitá e mutabilitá, Studi Economico–Giuridici della Facolta di Giurisprudenza dell Universitá di Cagliari, 1912 S.S.Gupta,Bibliography on the multivariate normal integrals and related topics.Ann. Math. Statist.,34(1963), pp. 829–838 M. E. Havrda, F. Charvát, Quantification method of classification processes: Concept of structuralα. Kybernetika, 3 (1975), pp. 30–35 J.P. Imhof, Computing the distribution of quadratic forms in normal variables. Biometrika, 48 (1961), pp. 419–426 D.R. Jensen, H. Solomon, A Gaussian approximation to the distribution of a definite quadratic form.J. Amer. Statist. Assoc., 67 (1972), pp. 898–902 N.L. Johnson, S. Kotz, Tables of distributions of positive definite quadratic forms in central normal variables. Sankhyā Ser. B, 30 (1968), pp. 303–314 J.N.Kapur,Measures of uncertainty, mathematical programming and physics. J. Ind. Soc. Agricultural Statist., 24 (1972), pp. 47–66 F. Liese, I. Vajda, Convex Statistical DistancesTeubner, Leipzig (1987) R. Modarres, R.W. Jernigan, Testing the equality of correlation matrices. Comm. Statist. Theory Methods, 21 (1992), pp. 2107–2125 D. Morales, L. Pardo, I. Vajda, Asymptotic divergence of estimates of discrete distributions. J. Statist. Plan. Inference (1995), pp. 347–369 L. Pardo, D. Morales, M. Salicrú, M.L. Menéndez, Rhφ-divergence statistics in applied categorical data analysis with stratified sampling. Utilitas Math., 44 (1993), pp. 145–164 M. C.Pardo,I.Vajda,About distances of discrete distributions satisfying the data process theorem of information theory. Trans. IEEE Inform. Theory, 43 (1997), pp. 1288–1293 M.C. Pardo, Asymptotic behaviour of an estimator based on Rao's divergence. Kybernetika, 33 (1997), pp. 489–504 K. Pearson, On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philos. Mag., 50 (1900), pp. 157–172 C.R. Rao, Diversity and dissimilarity coefficients: an unified approach. J. Theoret. Pop. Biol., 21 (1982), pp. 24–43 J.N.K. Rao, A.J. Scott, The analysis of categorical data from complex sample surveys: Chi-squared tests for goodness-of-fit and independence in two-way tables. J. Amer. Stat. Assoc., 76 (1981), pp. 221–230 T.R.C. Read, N. Cressie, Goodness of Fit Statistics for Discrete Multivariate DataSpringer-Verlag, New York (1988) F.E.Satterthwaite, An approximate distribution of estimates of variance components. Biometrics, 2 (1946), pp. 110–114 E.H. Simpson, Measurement of diversity. Nature, 163 (1949), p. 688 H. Solomon, Distribution of quadratic forms—tables and applications. Technical Report. Applied mathematics and statistics laboratories, Stanford University, Stanford, CA, 1960. I. Vajda, K. Vasek, Majorization, concave entropies, and comparison of experiments. Prob. Control Inform. Theory, 14 (1985), pp. 105–115 K. Zografos, K. Ferentinos, T. Papaioannou,ϕ-divergence statistics: Sampling properties and multinomial goodness of fit divergence tests. Comm. Statist. Theory Methods, 19 (1990), pp. 1785–1802
Collections