2020/09/13 by Miles E. Lopes, Lopes, Miles E. · 2 citations
Mathematics · Computer Science · #Mathematical Approximation and Integration #Bayesian Methods and Mixture Models #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2009.06004
Non-asymptotic bounds for Gaussian and bootstrap approximation have recently attracted significant interest in high-dimensional statistics. This paper studies Berry-Esseen bounds for such approximations with respect to the multivariate Kolmogorov distance, in the context of a sum of n random vectors that are p-dimensional and i.i.d. Up to now, a growing line of work has established bounds with mild logarithmic dependence on p. However, the problem of developing corresponding bounds with near n-1/2 dependence on n has remained largely unresolved. Within the setting of random vectors that have sub-Gaussian or sub-exponential entries, this paper establishes bounds with near n-1/2 dependence, for both Gaussian and bootstrap approximation. In addition, the proofs are considerably distinct from other recent approaches and make use of an "implicit smoothing" operation in the Lindeberg interpolation.