## Department Colloquium

### Friday, February 7th, 2020

**Time:** 2:30 p.m. **Place:** Jeffery Hall 234

**Speaker:** Natalia Stepanova (Carleton University)

**Title:** Goodness-of-fit tests based on sup-functionals of weighted empirical processes.

**Abstract: ** A large class of goodness-of-fit test statistics based on sup-functionals of weighted empirical processes is proposed and studied. The weight functions employed are Erdos-Feller-Kolmogorov-Petrovski upper-class functions of a Brownian bridge. Based on the result of M. Csorgo, S. Csorgo, Horvath, and Mason obtained for this type of test statistics, we provide the asymptotic null distribution theory for the class of tests in hand, and present an algorithm for tabulating the limit distribution functions under the null hypothesis. A new family of nonparametric confidence bands is constructed for the true distribution function and it is found to perform very well. The results obtained, together with a new result on the convergence in distribution of the higher criticism statistic, introduced by Donoho and Jin, demonstrate the advantage of our approach over a common approach that utilizes a family of regularly varying weight functions. Furthermore, we show that, in various subtle problems of detecting sparse heterogeneous mixtures, the proposed test statistics achieve the detection boundary found by Ingster and, when distinguishing between the null and alternative hypotheses, perform optimally adaptively to unknown sparsity and size of the non-null effects. This is joint work with Tatjana Pavlenko (Sweden).

**Natalia Stepanova** is a Professor of Statistics in the School of Mathematics and Statistics at Carleton University. She has a Ph.D. degree in Statistics from St. Petersburg State University. From 2001--2003 Natalia Stepanova was a Postdoctoral Fellow at Queen's University, supervised by Prof. Boris Levit. Her research interests lie mainly in the area of nonparametric statistics, including high-dimensional statistical inference.