**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.