Fetching the paper…
Reading the bibliography…
We explore properties of the $\chi^2$ and more general R\'enyi (Tsallis) distances to the normal law.
Cramér, H. On some classes of series used in mathematical statistics. Proc. 6th Scand. Math. Congr. Copenhagen, 1925, 399–425. See also: Harald Cramér. Collected works. Volume I, Ed. A. Martin-Löf, Springer-Verlag, 438–464
1925
Earlier work this paper cites.
Kullback, S., Leibler, R. A. On information and sufficiency. Ann. Math. Statistics 22 (1951), 79–86
1951
Earlier work this paper cites.
Prohorov, Yu. V. A local theorem for densities. (Russian) Doklady Akad. Nauk SSSR (N.S.) 83, (1952), 797–800
1952
Earlier work this paper cites.
Hirschman, I. I.; Widder, D. V. The convolution transform. Princeton University Press, Princeton, N. J., 1955. x+268 pp
1955
Earlier work this paper cites.
Linnik, Ju. V. An information-theoretic proof of the central limit theorem with the Lindeberg condition. Theory Probab. Appl. 4 (1959), 288–299
1959
Earlier work this paper cites.
Rényi, A. On measures of entropy and information. Proc. 4th Berkeley Sympos. Math. Statist. and Prob. Vol. I, pp. 547–561, 1961, Univ. California Press, Berkeley, Calif
1961
Earlier work this paper cites.
Sirazhdinov, S. H.; Mamatov, M. On mean convergence for densities. Theory Probab. Appl., 7 (1962), No. 4, 424–428
1962
Earlier work this paper cites.
Petrov, V. V. Local limit theorems for sums of independent random variables. (Russian) Teor. Verojatnost. i Primenen. 9 (1964), 343–352
1964
Earlier work this paper cites.
Pinsker, M. S. Information and information stability of random variables and processes. Translated and edited by Amiel Feinstein Holden-Day, Inc., San Francisco, Calif.-London-Amsterdam, 1964, xii+243 pp
1964
Earlier work this paper cites.
Csiszár, I. Information-type measures of difference of probability distributions and indirect observations. Studia Sci. Math. Hungar. 2 (1967), 299–318
1967
Earlier work this paper cites.
Kullback, S. A lower bound for discrimination in terms of variation. IEEE Trans. Inform. Theory, T-13, 1967, 126–127
1967
Earlier work this paper cites.
Ibragimov, I. A., Linnik, Yu. V. Independent and stationary sequences of random variables. With a supplementary chapter by I. A. Ibragimov and V. V. Petrov. Translation from the Russian edited by J. F. C. Kingman. Wolters-Noordhoff Publishing, Groningen, 1971, 443 pp
1971
Earlier work this paper cites.
Lieb, E. H. Some convexity and subadditivity properties of entropy. Bull. Amer. Math. Soc. 81 (1975), 1–13
1975
Earlier work this paper cites.
Petrov,V. V. Sums of Independent Random Variables. Berlin Heidelberg New York (1975)
1975
Earlier work this paper cites.
Barron, A. R. Entropy and the central limit theorem. Ann. Probab. 14 (1986), no. 1, 336–342
1986
Cited alongside, same era.
LeCam, L. M. Asymptotic Methods in Statistical Decision Theory. Springer Series in Statistics. Springer-Verlag, New York, 1986. xxvi+742 pp
1986
Cited alongside, same era.
Liese, F.; Vajda, I. Convex statistical distances. With German, French and Russian summaries. Teubner-Texte zur Mathematik [Teubner Texts in Mathematics], 95. BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1987. 224 pp
1987
Cited alongside, same era.
Vajda, I. Theory of Statistical Inference and Information. Kluwer Academic Publishers, Dordrecht-Borston-London, 1989, 432 pp
1989
Cited alongside, same era.
Amosova, N. N. Narrow zones of local normal attraction. (Russian) Teor. Veroyatnost. i Primenen. 35 (1990), no. 1, 138–143. Translation in: Theory Probab. Appl. 35 (1990), no. 1, 140–145 (1991)
Artstein, S.; Ball, K. M.; Barthe, F.; Naor, A. On the rate of convergence in the entropic central limit theorem. Probab. Theory Related Fields 129 (2004), no. 3, 381–390
2004
Later among the works it cites.
Barron, A. R.; Johnson, O. Fisher information inequalities and the central limit theorem. Probab. Theory Related Fields 129 (2004), no. 3, 391–409
2004
Later among the works it cites.
Johnson, O. Information theory and the central limit theorem. Imperial College Press, London, 2004, xiv+209 pp
2004
Later among the works it cites.
Bobkov, S. G.; Houdré, C.; Tetali, P. The subgaussian constant and concentration inequalities. Israel J. Math. 156 (2006), 255–283
2006
Later among the works it cites.
Bhattacharya, R. N.; Ranga Rao, R. Normal approximation and asymptotic expansions. John Wiley & Sons, Inc. 1976. Also: Soc. for Industrial and Appl. Math., Philadelphia, 2010
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
1991
Cited alongside, same era.
Amosova, N. N. A remark on a local limit theorem for large deviations. (Russian) Teor. Veroyatnost. i Primenen. 35 (1990), no. 4, 754–756. Translation in: Theory Probab. Appl. 35 (1990), no. 4, 758–760 (1991)
1991
Cited alongside, same era.
Carlen, E. A. Superadditivity of Fisher’s information and logarithmic Sobolev inequalities. J. Funct. Anal. 101 (1991), no. 1, 194–211
1991
Cited alongside, same era.
Dembo, A., Cover, T. M., Thomas, J. A. Information-theoretic inequalities. IEEE Trans. Inform. Theory, 37 (1991), no. 6, 1501–1518
1991
Cited alongside, same era.
Shiryaev, A. N. Probability. Sspringer-Verlag, 1996
1996
Cited alongside, same era.
Borland, L.; Plastino, A. R.; Tsallis, C. Information gain within nonextensive thermostatistics. J. Math. Phys. 39 (1998), no. 12, 6490–6501
1998
Cited alongside, same era.
Tsallis, C. Generalized entropy-biased criterion for consistent testing. Phys. Rev. E 58 (1998), 1442–1445
1998
Cited alongside, same era.
Bobkov, S. G.; Götze, F. Exponential integrability and transportation cost related to logarithmic Sobolev inequalities. J. Funct. Anal. 163 (1999), no. 1, 1–28
1999
Cited alongside, same era.
2010
Later among the works it cites.
Gilardoni, G. L. On Pinsker’s and Vajda’s type inequalities for Csiszar’s
2010
Later among the works it cites.
Bobkov, S. G.; Chistyakov, G. P.; Götze, F. Non-uniform bounds in local limit theorem in case of fractional moments. I. Math. Methods of Statistics, 20 (2011), no. 3, 171–191; II. Math. Methods of Statistics, 20 (2011), no. 4, 269–287
2011
Later among the works it cites.
Bobkov, S. G.; Chistyakov, G. P.; Götze, F. Rate of convergence and Edgeworth-type expansion in the entropic central limit theorem. Ann. Probab. 41 (2013), no. 4, 2479–2512
2013
Later among the works it cites.
Nielsen, F. On the Chi square and higher-order Chi distances for approximating
2013
Later among the works it cites.
Bobkov, S. G.; Chistyakov, G. P.; Götze, F. Berry-Esseen bounds in the entropic central limit theorem. Probab. Theory Related Fields 2014 (159), 435–478
2014
Later among the works it cites.
Bobkov, S. G.; Chistyakov, G. P.; Götze, F. Fisher information and the central limit theorem. Probab. Theory Related Fields 159 (2014), issue 1-2, 1–59
2014
Later among the works it cites.
van Erven, T., Harremoës, P. Rényi divergence and Kullback-Leibler divergence. IEEE Trans. Inform. Theory 60 (2014), no. 7, 3797–3820
2014
Later among the works it cites.
Bobkov, S. G.; Chistyakov, G. P.; Kösters, H. The entropic Erdös-Kac limit theorem. J. Theor. Probab. 28 (2015), no. 4, 1520–1555
2015
Later among the works it cites.
Bally, V.; Caramellino, L. Asymptotic development in the CLT in total variation distance. Bernoulli 22 (2016), 2442–2485
2016
Closest in time.