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Original Articles

An improvement of a non-uniform bound for combinatorial central limit theorem

, &
Pages 2129-2146 | Received 15 Sep 2017, Accepted 11 Mar 2018, Published online: 16 Apr 2018

References

  • Bolthausen, E. 1984. An estimate of the remainder in a combinatorial central limit theorem. Probability Theory and Related Fields 66 (3):379–86.
  • Chaidee, N. 2005. Non-uniform bounds in normal approximation for matrix correlation statistics and independent bounded random variables. PhD's Thesis, Department of Mathematics, Faculty of Science, Chulalongkorn University.
  • Chen, L. H. Y., and X. Fang. 2015. On the error bound in a combinatorial central limit theorem. Bernoulli 21 (1):335–59.
  • Chen, L. H. Y., L. Goldstein, and Q. M. Shao. 2011. Normal approximation by Stein's method. Heidelberg, Dordrecht, London, New York: Springer Science & Business Media.
  • Chen, L. H. Y., and Q. M. Shao. 2001. A non-uniform Berry–Esseen bound via Stein's method. Probability Theory and Related Fields 120 (2):236–54.
  • Chen, L. H., and Q. M. Shao. 2005. Stein's method for normal approximation. An Introduction to Stein's Method 4:1–59.
  • Chumpong, K. 2014. Non-uniform bound for combinatorial central limit theorem. Master Thesis, Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University.
  • Does, R. J. M. M. 1982. Berry-Esseen theorem for simple linear rank statistics under the null-hypothesis. Ann. Probability. 10 (4):982–91.
  • Fraser, D. A. 1957. Nonparametric methods in statistics. New york: John Wiley.
  • Frolov, A. N. 2014. Esseen type bounds of the remainder in a combinatorial CLT. Journal Statistical Planning and Inference 149:90–97.
  • Frolov, A. N. 2015. Bounds of the remainder in a combinatorial central limit theorem. Statist. Probab. Letters 105:37–46.
  • Goldstein, L. 2005. Berry-Esseen bounds for combinatorial central limit theorems and pattern occurrences, using zero and size biasing. Journal of Applied Probability 42 (3):661–83.
  • Ho, S. T., and L. H. Y. Chen. 1978. An Lp bound for the remainder in a combinatorial central limit theorem. The Annals of Probability 6 (2):231–49.
  • Hoeffding, W. 1951. A combinatorial central limit theorem. The Annals of Mathematical Statistics 22 (4):558–66.
  • Ibragimov, M., and R. Ibragimov. 2008. Optimal constants in the Rosenthal inequality for random variables with zero odd moments. Statistics and Probability Letters 78 (2):186–9.
  • Ibragimov, R., and S. Sharakhmetov. 2001. The best constant in the Rosenthal inequality for nonnegative random variables. Statistics and probability letters 55 (4):367–76.
  • Ibragimov, R., and S. Sharakhmetov. 2002. The exact constant in the Rosenthal inequality for random variables with mean zero. Theory of Probability and Its Applications 46 (1):127–32.
  • Latala, R. 1997. Estimation of moments of sums of independent real random variables. The Annals of Probability 25 (3):1502–13.
  • Neammanee, K., and P. Rattanawong. 2009. Non-uniform bound on normal approximation of Latin hypercube sampling. Journal of Mathematics Research 1 (2):28–42.
  • Neammanee, K., and N. Rerkruthairat. 2012. An improvement of a uniform bound on a combinatorial central limit theorem. Communications in Statistics-Theory and Methods 41 (9):1590–602.
  • Neammanee, K., and J. Suntornchost. 2005. A uniform bound on a combinatorial central limit theorem. Stochastic Analysis and Applications 23 (3):559–78.
  • Puri, M. L., and P. K. Sen. 1971. Nonparametric methods in multivariate analysis. New york: John Wiley.
  • Rosenthal, H. P. 1970. On the subspaces of Lp(p > 2) spanned by sequences of independent random variables. Israel Journal of Mathematics 8 (3):273–303.
  • Simcharoen, W., and K. Neammanee. 2016. Non-uniform bound on a combinatorial central limit theorem. Communications in Statistics-Theory and Methods 45 (18):5517–32.
  • Stein, C. 1986. Approximate computation of expectations. Lecture Notes-Monograph Series, 7. Hayward, CA: IMS.
  • von Bahr, B. 1976. Remainder term estimate in a combinatorial limit theorem. Probability Theory and Related Fields 35 (2):131–9.
  • Wald, A., and J. Wolfowitz. 1944. Statistical tests based on permutations of the observations. The Annals of Mathematical Statistics 15 (4):358–72.

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