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arXiv · 1505.03199

On Strong Embeddings by Stein's Method

Chinmoy Bhattacharjee·Larry Goldstein
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Abstract

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.

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Chinmoy Bhattacharjee, Larry Goldstein. 2015-05-13. On Strong Embeddings by Stein's Method. https://doi.org/10.1214/16-ejp4299

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