ABSTRACT

Asymptotic analysis and orthogonal polynomials have been extensively studied for over two centuries, with deep connections to various fields, including number theory, combinatorics, differential equations, numerical integration, and random matrix theory. In this talk, we will explore their applications in parallel computation and statistical inference. Specifically, we will estimate the condition number of a Vandermonde-type matrix arising in the time discretization of initial value problems. Additionally, we will examine the asymptotic distributions of weighted cumulative sum statistics for change-point detection and the likelihood functions of Poisson-lognormal mixed models.