On strong embeddings by Stein’s method
Copyright policy )On strong embeddings by Stein’s method
Strong embeddings, that is, couplings between a partial sum process of a sequence of random variables and a Brownian motion, have found numerous applications in probability and statistics. We extend Chatterjee's novel use of Stein's method for $\{-1,+1\}$ valued variables to a general class of discrete distributions, and provide $\log n$ rates for the coupling of partial sums of independent variables to a Brownian motion, and results for coupling sums of suitably standardized exchangeable variables to a Brownian bridge.
Typos and minor corrections made to Lemma 2.6
- University of Southern California United States
- University of California System United States
zero bias, 60F05, 60F17, 60G09, Probability (math.PR), exchangeability, strong approximation, 60G09, 60F17, 60F05, FOS: Mathematics, coupling, Mathematics - Probability
zero bias, 60F05, 60F17, 60G09, Probability (math.PR), exchangeability, strong approximation, 60G09, 60F17, 60F05, FOS: Mathematics, coupling, Mathematics - Probability
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