## Joint Seminars in Statistics & Biostatistics

### Wednesday, November 6th, 2019

**Time:** 11:30-12:30** Place:** Jeffery Hall 225

**Speaker:** Yanglei Song (Queen's University)

**Abstract:** I will start with a discussion on the recent development in the normal approximation (a.k.a. central limit theorem) and bootstrap for the sum of high dimensional random vectors, empirical processes and U-processes. Statistical applications will also be provided. Then I will talk about a piece of ongoing work in this line, with Xiaohui Chen and Kengo Kato. Its abstract is as follows: This paper studies the non-asymptotic inference for the supremum of an incomplete, non-degenerate U-process. The process is indexed by a function class of order r, whose complexity possibly increases with the sample size n. For each function, its corresponding U-statistic involves the average of O(n^r) numbers, which is prohibitively demanding even for moderate r. Thus we study its incomplete version, where each subsample of size r is included in the average with a very small probability. We first approximate the supremum of such incomplete U-process by that of an appropriate Gaussian process in the Kolmogorov distance and then propose valid bootstrap methods to address the practical issue of unknown covariance function. Finally, we discuss its application in testing the qualitative features, such as convexity, of nonparametric functions.