Research articles
ScienceAsia 44 (2018): 277-287 |doi:
10.2306/scienceasia1513-1874.2018.44.277
Exponential bounds via Stein’s method and exchangeable pairs
Patcharee Sumritnorrapong, Kritsana Neammanee, Jiraphan Suntornchost*
ABSTRACT: We apply Stein’s 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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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
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