A1301
Title: High-dimensional bootstrap and asymptotic expansion
Authors: Yuta Koike - University of Tokyo (Japan) [presenting]
Abstract: Recent work has shown that bootstrap approximation for The maximum of a sum of independent random vectors is justified even when The dimension is much larger than The sample size. In this context, numerical experiments suggest that third-moment matching bootstrap approximations outperform normal approximation even without studentization, but existing theoretical results cannot explain this phenomenon. An asymptotic expansion formula for The bootstrap coverage probability is developed and shown to explain The phenomenon. In particular, a blessing of dimensionality phenomenon is identified: The third-moment matching wild bootstrap is second-order accurate in high dimensions even without studentization if The covariance matrix has identical diagonal entries and bounded eigenvalues. The validity of these results is established under The assumption that The underlying distributions admit Stein kernels.
