Advertisement

Accuracy of Central Limit Theorems

  • Anirban DasGupta
Part of the Springer Texts in Statistics book series (STS)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bentkus, V. (2003). On the dependence of the Berry-Esseen bound on dimension, J. Stat. Planning Infer., 113(2), 385–402.zbMATHCrossRefMathSciNetGoogle Scholar
  2. Berry, A.C. (1941). The accuracy of the Gaussian approximation to the sum of independent variates, Trans. Am. Math. Soc., 49, 122–136.zbMATHCrossRefMathSciNetGoogle Scholar
  3. Bhattacharya, R.N. and Rao, R.R. (1986). Normal Approximation and Asymptotic Expansions, Robert E. Krieger, Melbourne, FL.zbMATHGoogle Scholar
  4. Esseen, C. (1945). Fourier analysis of distribution functions: a mathematical study, Acta Math., 77, 1–125.zbMATHCrossRefMathSciNetGoogle Scholar
  5. Feller, W. (1966). An Introduction to Probability Theory with Applications, John Wiley, New York.Google Scholar
  6. Göetze, F. (1991). On the rate of convergence in the multivariate CLT, Ann. Prob., 19(2), 724–739.CrossRefGoogle Scholar
  7. Michel, R. (1981). On the constant in the nonuniform version of the Berry-Esseen theorem, Z. Wahr. Verw. Geb., 55(1), 109–117.zbMATHCrossRefGoogle Scholar
  8. Petrov, V. (1975). Limit Theorems for Sums of Independent Random Variables (translation from Russian), Springer-Verlag, New York.Google Scholar
  9. Senatov, V. (1998). Normal Approximations: New Results, Methods and Problems, VSP, Utrecht.zbMATHGoogle Scholar
  10. Serfling, R. (1980). Approximation Theorems of Mathematical Statistics, John Wiley, New York.zbMATHGoogle Scholar
  11. van der Vaart, A. and Wellner, J. (1996). Weak Convergence and Empirical Processes, with Applications to Statistics, Springer-Verlag, New York.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Anirban DasGupta
    • 1
  1. 1.Department of StatisticsPurdue UniversityWest Lafayette

Personalised recommendations