Non-classical Berry-Esseen inequality and accuracy of the weighted bootstrap

Abstract: In this talk, we will study higher-order accuracy of the weighted bootstrap procedure for estimation of a distribution of a sum of independent random vectors with bounded fourth moments, on the set of all Euclidean balls. Our approach is based on Berry-Esseen type inequality which extends the classical normal approximation bound. These results justify in non-asymptotic setting that the weighted bootstrap can outperform Gaussian (or chi-squared) approximation in accuracy w.r.t. dimension and sample size. In addition, the presented results lead to improvements of accuracy of a weighted bootstrap procedure for general log-likelihood ratio statistics (under certain regularity conditions). The theoretical results will be illustrated with numerical experiments on simulated data.
Biography: Mayya Zhilova is an Assistant Professor in the School of Mathematics at Georgia Institute of Technology. She received her PhD in Mathematical Statistics from Humboldt University of Berlin in 2015, and diploma in Mathematics from Lomonosov Moscow State University in 2010. Her research interests lie in the areas of statistical inference for high-dimensional data, resampling methods, and applied probability.