Statistics Seminar: Higher-order Berry-Esseen inequalities and accuracy of the bootstrap

When:
September 22, 2017 @ 3:00 pm – 4:00 pm
2017-09-22T15:00:00-04:00
2017-09-22T16:00:00-04:00
Where:
M&S Seminar Room 1441
25 Park Place
Atlanta, GA 30303
USA
Contact:
Yichuan Zhao

Title
Higher-order Berry-Esseen inequalities and accuracy of the bootstrap

Speaker
Dr. Mayya Zhilova, Assistant Professor, School of Mathematics, Georgia Institute of Technology

Abstract
In this talk, we study higher-order accuracy of a bootstrap procedure for approximation in distribution of a smooth function of a sample average in high-dimensional non-asymptotic framework. Our approach is based on Berry-Esseen type inequalities which extend the classical normal approximation bounds. These results justify in non-asymptotic setting that bootstrapping can outperform Gaussian (or chi-squared) approximation in accuracy with respect to both 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 are illustrated with numerical experiments on simulated data.