Spring 2022

Xiongzhi Chen

Title: Proportion estimation, probability, integral equations, and harmonic analysis

Abstract: Estimating the “signal proportion’’ is a very important task in statistical learning of high-dimensional data, and in particular, for multiple hypothesis testing. However, this is not an easy task when we want to design estimators that are able to consistently estimate such a proportion when random variables encoding it are not identically distributed. In this talk, I will propose consistent estimators under these settings from the perspective of Lebesgue-Stieltjes integral equations and harmonic analysis on Abelian groups, and illustration how these estimators connect the aforementioned two subfields of mathematics, as well as statistics and probability theory.