B0814
Title: High-dimensional CLT with general covariance structure
Authors: Yuta Koike - University of Tokyo (Japan) [presenting]
Xiao Fang - The Chinese University of Hong Kong (Hong Kong)
Abstract: The focus is on the problem of bounding the normal approximation error over rectangles for a sum of n independent d-dimensional random vectors. We aim to establish such a bound with poly-logarithmic dependence on the dimension d. It is known that such a bound is available with a nearly $n^(-1/2)$ convergence rate when the covariance matrix of the sum is non-degenerate. We show that, under some additional distributional assumptions such as log-concavity, we can derive error bounds with nearly $n^(-1/2)$ convergence rates and poly-log dependence on d without any restriction on the covariance matrix. We also discuss whether these improved normal approximation error rates can be transferred to bootstrap approximation.
