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Research articles

ScienceAsia 44 (2018): 277-287 |doi: 10.2306/scienceasia1513-1874.2018.44.277

Exponential bounds via Steinís method and exchangeable pairs

Patcharee Sumritnorrapong, Kritsana Neammanee, Jiraphan Suntornchost*

ABSTRACT:     We apply Steinís method to obtain a non-uniform exponential bound for normal approximations for certain types of random variables. In particular, we establish the bound for a random variable such that its exchangeable pair coupling exists and the distance between the pair is bounded. Using our result, we obtain better bounds for a wide range of applications, such as sums of bounded independent random variables, the combinatorial central limit theorem, and the numbers of descents and inversions of a permutation.

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a Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330 Thailand

* Corresponding author, E-mail: Jiraphan.S@chula.ac.th

Received 21 Jun 2017, Accepted 21 Jul 2018