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Accuracy of Central Limit Theorems

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References

  • Bentkus, V. (2003). On the dependence of the Berry-Esseen bound on dimension, J. Stat. Planning Infer., 113(2), 385–402.

    Article  MATH  MathSciNet  Google Scholar 

  • Berry, A.C. (1941). The accuracy of the Gaussian approximation to the sum of independent variates, Trans. Am. Math. Soc., 49, 122–136.

    Article  MATH  MathSciNet  Google Scholar 

  • Bhattacharya, R.N. and Rao, R.R. (1986). Normal Approximation and Asymptotic Expansions, Robert E. Krieger, Melbourne, FL.

    MATH  Google Scholar 

  • Esseen, C. (1945). Fourier analysis of distribution functions: a mathematical study, Acta Math., 77, 1–125.

    Article  MATH  MathSciNet  Google Scholar 

  • Feller, W. (1966). An Introduction to Probability Theory with Applications, John Wiley, New York.

    Google Scholar 

  • Göetze, F. (1991). On the rate of convergence in the multivariate CLT, Ann. Prob., 19(2), 724–739.

    Article  Google Scholar 

  • Michel, R. (1981). On the constant in the nonuniform version of the Berry-Esseen theorem, Z. Wahr. Verw. Geb., 55(1), 109–117.

    Article  MATH  Google Scholar 

  • Petrov, V. (1975). Limit Theorems for Sums of Independent Random Variables (translation from Russian), Springer-Verlag, New York.

    Google Scholar 

  • Senatov, V. (1998). Normal Approximations: New Results, Methods and Problems, VSP, Utrecht.

    MATH  Google Scholar 

  • Serfling, R. (1980). Approximation Theorems of Mathematical Statistics, John Wiley, New York.

    MATH  Google Scholar 

  • van der Vaart, A. and Wellner, J. (1996). Weak Convergence and Empirical Processes, with Applications to Statistics, Springer-Verlag, New York.

    MATH  Google Scholar 

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DasGupta, A. (2008). Accuracy of Central Limit Theorems. In: Asymptotic Theory of Statistics and Probability. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-75971-5_11

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