References

• Afendras, G.; Papadatos, N.; Papathanasiou, V. : An extended Stein-type covariance identity for the Pearson family with applications to lower variance bounds. Bernoulli 17 (2011), no. 2, 507--529. MR2787602
• Barbour, A. D. : Stein's method for diffusion approximations. Probab. Theory Related Fields 84 (1990), no. 3, 297--322. MR1035659
• Barbour, A. D., and Chen, L. H. Y.: An introduction to Stein's method, vol. 4. World Scientific, 2005. MR2205339
• Barbour, A. D., and Chen, L. H. Y.: Stein's method and applications, vol. 5. World Scientific, 2005. MR2205339
• Barbour, A. D.; Johnson, O.; Kontoyiannis, I.; Madiman, M. : Compound Poisson approximation via information functionals. Electron. J. Probab. 15 (2010), 1344--1368. MR2721049
• Barron, Andrew R. : Entropy and the central limit theorem. Ann. Probab. 14 (1986), no. 1, 336--342. MR0815975
• Brown, Lawrence D. : A proof of the central limit theorem motivated by the Cramér-Rao inequality. Statistics and probability: essays in honor of C. R. Rao, pp. 141--148, North-Holland, Amsterdam-New York, 1982. MR0659464
• Cacoullos, T.; Papathanasiou, V. : Characterizations of distributions by variance bounds. Statist. Probab. Lett. 7 (1989), no. 5, 351--356. MR1001133
• Cacoullos, T.; Papathanasiou, V.; Utev, S. A. : Variational inequalities with examples and an application to the central limit theorem. Ann. Probab. 22 (1994), no. 3, 1607--1618. MR1303658
• Chatterjee, Sourav; Fulman, Jason; Röllin, Adrian : Exponential approximation by Stein's method and spectral graph theory. ALEA Lat. Am. J. Probab. Math. Stat. 8 (2011), 197--223. MR2802856
• Chatterjee, Sourav; Shao, Qi-Man : Nonnormal approximation by Stein's method of exchangeable pairs with application to the Curie-Weiss model. Ann. Appl. Probab. 21 (2011), no. 2, 464--483. MR2807964
• Chen, Louis H. Y.; Goldstein, Larry; Shao, Qi-Man : Normal approximation by Stein's method. Probability and its Applications (New York). Springer, Heidelberg, 2011. xii+405 pp. ISBN: 978-3-642-15006-7 MR2732624
• Chen, Louis H. Y.; Shao, Qi-Man : Stein's method for normal approximation. An introduction to Stein's method, 1--59, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., 4, Singapore Univ. Press, Singapore, 2005. MR2235448
• Cover, Thomas M.; Thomas, Joy A. : Elements of information theory. Second edition. Wiley-Interscience [John Wiley & Sons], Hoboken, NJ, 2006. xxiv+748 pp. ISBN: 978-0-471-24195-9; 0-471-24195-4 MR2239987
• Döbler, C.: Stein's method of exchangeable pairs for absolutely continuous, univariate distributions with applications to the polya urn model. arXiv:1207.0533, July 2012.
• Gibbs, A. L., and Su, F. E.: On choosing and bounding probability metrics. International Statistical Review / Revue Internationale de Statistique, 70 (2002), 419--435.
• Goldstein, Larry; Reinert, Gesine : Distributional transformations, orthogonal polynomials, and Stein characterizations. J. Theoret. Probab. 18 (2005), no. 1, 237--260. MR2132278
• Goldstein, Larry; Reinert, Gesine : Stein's method and the beta distribution. arXiv:1207.1460, July 2012.
• Götze, F. : On the rate of convergence in the multivariate CLT. Ann. Probab. 19 (1991), no. 2, 724--739. MR1106283
• Johnson, Oliver : Information theory and the central limit theorem. Imperial College Press, London, 2004. xiv+209 pp. ISBN: 1-86094-473-6 MR2109042
• Johnson, Oliver; Barron, Andrew : Fisher information inequalities and the central limit theorem. Probab. Theory Related Fields 129 (2004), no. 3, 391--409. MR2128239
• Kontoyiannis, Ioannis; Harremoës, Peter; Johnson, Oliver : Entropy and the law of small numbers. IEEE Trans. Inform. Theory 51 (2005), no. 2, 466--472. MR2236061
• Ley, C., and Swan, Y.: Stein's density approach for discrete distributions and information inequalities. arXiv:1211.3668v1, November 2012.
• Linnik, Ju. V. : An information-theoretic proof of the central limit theorem with Lindeberg conditions. (Russian) Theor. Probability Appl. 4 1959 288--299. MR0124081
• Luk, H. M.: Stein's method for the gamma distribution and related statistical applications. PhD thesis, University of Southern California, 1994.
• Mayer-Wolf, Eduardo : The Cramér-Rao functional and limiting laws. Ann. Probab. 18 (1990), no. 2, 840--850. MR1055436
• Nourdin, Ivan; Peccati, Giovanni : Stein's method meets Malliavin calculus: a short survey with new estimates. Recent development in stochastic dynamics and stochastic analysis, 207--236, Interdiscip. Math. Sci., 8, World Sci. Publ., Hackensack, NJ, 2010. MR2807823
• Nourdin, Ivan; Peccati, Giovanni : Normal approximations with Malliavin calculus. From Stein's method to universality. Cambridge Tracts in Mathematics, 192. Cambridge University Press, Cambridge, 2012. xiv+239 pp. ISBN: 978-1-107-01777-1 MR2962301
• Picket, A.: Rates of convergence of χ^2 approximations via Stein's method. PhD thesis, Lincoln College, University of Oxford, 2004.
• Röllin, A.: On the optimality of stein factors. phProbability Approximations and Beyond/ (2012), ~61--72.
• Ross, Nathan : Fundamentals of Stein's method. Probab. Surv. 8 (2011), 210--293. MR2861132
• Sason, I.: An information-theoretic perspective of the poisson approximation via the chen-stein method. pharXiv:1206.6811/, June 2012.
• Sason, I.: On the entropy of sums of bernoulli random variables via the chen-stein method. pharXiv:1207.0436/, July 2012.
• Schoutens, Wim: Orthogonal polynomials in Stein's method. J. Math. Anal. Appl. 253 (2001), no. 2, 515--531. MR1808151
• Shimizu, R.: On fisher's amount of information for location family. In phStatistical Distributions in Scientific Work/ (1975), G. P. et~al., Ed., vol. 3, ~305--312.
• Shimizu, Ryoichi: Error bounds for asymptotic expansion of the scale mixtures of the normal distribution. Ann. Inst. Statist. Math. 39 (1987), no. 3, 611--622. MR0930533
• Stein, Charles: A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. II: Probability theory, pp. 583--602. Univ. California Press, Berkeley, Calif., 1972. MR0402873
• Stein, Charles: Approximate computation of expectations. Institute of Mathematical Statistics Lecture Notes—Monograph Series, 7. Institute of Mathematical Statistics, Hayward, CA, 1986. iv+164 pp. ISBN: 0-940600-08-0 MR0882007
• Stein, Charles; Diaconis, Persi; Holmes, Susan; Reinert, Gesine: Use of exchangeable pairs in the analysis of simulations. Stein's method: expository lectures and applications, 1--26, IMS Lecture Notes Monogr. Ser., 46, Inst. Math. Statist., Beachwood, OH, 2004. MR2118600
• Stein, Charles M.: Estimation of the mean of a multivariate normal distribution. Ann. Statist. 9 (1981), no. 6, 1135--1151. MR0630098