**Title**

\nHigher-order Berry-Esseen inequal
ities and accuracy of the bootstrap

**Speaker**

\nDr. Mayya Zhilova\, Assistant Professor\, School of Mathematics\, Georgi
a Institute of Technology

**Abstract**

\nIn this
talk\, we study higher-order accuracy of a bootstrap procedure for approx
imation in distribution of a smooth function of a sample average in high-d
imensional 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 ou
tperform Gaussian (or chi-squared) approximation in accuracy with respect
to both dimension and sample size. In addition\, the presented results lea
d to improvements of accuracy of a weighted bootstrap procedure for genera
l log-likelihood ratio statistics (under certain regularity conditions). T
he theoretical results are illustrated with numerical experiments on simul
ated data.