Statistics Seminar: Higher-order Berry-Esseen inequalities and accuracy of the bootstrap
Higher-order Berry-Esseen inequalities and accuracy of the bootstrap
Dr. Mayya Zhilova, Assistant Professor, School of Mathematics, Georgia Institute of Technology
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.