Second and Higher Order Statistical Methods in Some Once Differentiable Problems

Explore advanced statistical methods in this 46-minute lecture by Cun Hui Zhang, presented at the International Mathematical Union. Delve into second and higher order statistical inference techniques for once differentiable problems, focusing on three key examples. Examine how second order Stein's formula corrects bias in high-dimensional linear regression, and learn about the application of scaled Mallow's C_{p} for estimator selection. Investigate bootstrap methods for approximating distributions of component-wise maximums in high-dimensional scenarios, including recent developments using un-smoothed maximum interpolation. Finally, discover a high order unbiased statistical expansion for estimating functionals of high-dimensional mean vectors, providing optimal convergence rates for various non-smooth additive functionals. Gain insights into cutting-edge statistical techniques and their applications in complex mathematical problems.