**Title**

\nHigher
-order Berry-Esseen inequalities and accuracy of the bootstrap

\nDr. Mayya Zhilova\, Assistant Professor\, Sch
ool of Mathematics\, Georgia Institute of Technology

**Abstr
act**

\nIn this talk\, we study higher-order accuracy of a boo
tstrap procedure for approximation in distribution of a smooth function of
a sample average in high-dimensional non-asymptotic framework. Our approa
ch is based on Berry-Esseen type inequalities which extend the classical n
ormal approximation bounds. These results justify in non-asymptotic settin
g that bootstrapping can outperform Gaussian (or chi-squared) approximatio
n in accuracy with respect to both dimension and sample size. In addition\
, the presented results lead to improvements of accuracy of a weighted boo
tstrap procedure for general log-likelihood ratio statistics (under certai
n regularity conditions). The theoretical results are illustrated with num
erical experiments on simulated data.