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For testing goodness of fit it is very popular to use either the chi square statistic or G statistics (information divergence).
I. Csiszár, “Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der ergodizität von Markoffschen Ketten,” Publ. Math. Inst. Hungar. Acad
1963
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R. R. Sokal and R. J. Rohlf, Biometry: the principles and practice of statistics in biological research · 1981
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M. P. Quine and J. Robinson, “Efficiencies of chi-square and likelihood ratio goodness-of-fit tests.,” Ann. Statist
1985
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J. Chen and H. Rubin, “Bounds for the difference between median and mean of Gamma and Poisson distributions,” Statistics and Probability Letters
1986
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P. W. Glynn, “Upper bounds on Poisson tail probabilities,” Operations Research Letters
1987
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O. E. Barndorff-Nielsen and P. Hall, “On the level-error after Bartlett adjustment of the likelihood-ratio statistic,” Biometrika
1988
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T. Dunning, “Accurate methods for the statistics of surprise and coincidence,” Computational Linguistics
1993
Cited alongside, same era.
Chapman and Hall, 1994
O. E. Barndorff-Nielsen and D. R. Cox, Inference and asymptotics · 1994
Cited alongside, same era.
K. Hamza, “The smallest uniform upper bound on the distance between the mean and the median of the binomial and Poisson distributions,” Statistics and Probability Letters
1995
Cited alongside, same era.
Cambridge University Press, 1998
B. S. Everitt, The Cambridge Dictionary of Statistics · 1998
Cited alongside, same era.
L. Györfi, G. Morvai, and I. Vajda, “Information-theoretic methods in testing the goodness-of-fit,” in Proc. International Symposium on Information Theory, Sorrento, Italy, June25-30
2000
Cited alongside, same era.
New York: Springer, 3rd ed. ed., 2005
E. Lehman and G. Castella, Testing Statistical Hypotheses · 2005
Later among the works it cites.
T. Zhang, “Limiting distribution of the G statistics,” Statistics and Probability Letters
2008
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P. Harremoës and I. Vajda, “On the Bahadur-efficient testing of uniformity by means of the entropy,” IEEE Trans. Inform Theory
2008
Later among the works it cites.
P. Harremoës and I. Vajda, “Efficiency of entropy testing,” in International Symposium on Information Theory
2008
Later among the works it cites.
2011
Later among the works it cites.
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J. Beirlant, L. Devroye, L. Györfi, and I. Vajda, “Large deviations of divergence measures on partitions,” J. Statist. Planning and Infer
2001
Cited alongside, same era.
L. Györfi, P. Harremoës, and G. Tusnády, “Gaussian approximation of large deviation probabilities.” Submitted for presentation at ITW, 2012
2012
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