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Original Articles

Bounds on Normal Approximations for the number of Descents and Inversions

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Pages 2310-2329 | Received 24 Sep 2012, Accepted 15 Feb 2013, Published online: 22 Jun 2015

References

  • Barbour, A.D., Chen, L. H.Y. (2005). An Introduction to Stein’s Method. Singapore: Singapore University Press.
  • Bender, E. (1973). Central and local limit theorems applied to asymtotic enumeration. J. Combin. Theory Ser. A 15:91–111.
  • Chen, L. H.Y., Shao, Q.M. (2001). A non-uniform Berry-Esseen bound via Stein’s method. Probab. Theory Relat. Fields 120:236–254.
  • Diaconis, P. (1988). Group Representations in Probability and Statistics. Hayward, CA:Institute of Mathematical Statistics Lecture Notes.
  • Fulman, J. (2004). Stein’s method and non-reversible Markov chains. In: Diaconis, P., Holmes, S., eds., Stein’s Method: Expository Lectures and Applications, pp. 66–74. Beachwood, OH:Institute of Mathematical Statistics.
  • Neammanee, K., Laipaporn, K. (2008). A uniform bound on a combinatorial central limit theorem for randomized orthogonal array sampling designs. Stoch. Anal. Appl. 26:243–255.
  • Neammanee, K., Rattanawong, P. (2008). A uniform bound on the generalization of a combinatorial central limit theorem. Int. Math. Forum 3:11–27.
  • Neammanee, K., Rattanawong, P. (2009). Non-uniform bound on normal approximation of Latin hypercube sampling. JMR 1:28–42.
  • Pitman, J. (1997). Probabilistic bounds on the coefficients of polynomials with only real zero. J. Combin. Theory Ser. A 77:279–303.
  • Rinott, Y., Rotar, V. (1997). On coupling constructions with rates in the CLT for dependent summands with applications to the antivoter model and weighted U-statistics. Ann. Appl. Probab. 7:1080–1105.
  • Stein, C. (1972). A bound for the error in the normal approximation to the distribution of a sum of independent random variables. Proc. Sixth Berkeley Symp. Math. Statist. Probab. University of California Press. Berkeley, California, 2:583–602.
  • Stein, C. (1986). Approximate computation of expectation. IMS, Hayward, CA.
  • Tanny, S. (1973). A probabilistic interpretation of Eulerian numbers. Duke Math J. 40:717–722.

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