Nonasymptotic Edgeworth-Type Expansions for Growing Dimension

Speaker: Mayya Zhilova, George Tech

Abstract: In this talk I would like to discuss the problem of establishing higher order accuracy of bootstrapping procedures and (non-)normal approximation in the multivariate or high-dimensional setting. This topic is important for numerous problems in statistical inference and applications concerned with confidence estimation and hypothesis testing, and involving a growing dimension of random data or unknown parameter. In particular, I will focus on higher-order expansions for the uniform distance over the set of all Euclidean balls. The talk will include an overview of main ideas in the proofs, and examples of statistical problems where the new results lead to improvements in accuracy of approximation. The talk is based on the results in the recent preprint https://arxiv.org/abs/2006.03959, and https://arxiv.org/abs/1611.02686