DMS Applied Mathematics Seminar

Speaker: Hans-Werner van Wyk

Title: Clenshaw-Curtis Type Rules for Statistical Integrals

Abstract: In statistics, many commonly encountered quantities take the form of density weighted integrals. This talk treats their numerical estimation within the Chebyshev approximation framework. In particular, we discuss how a generic one dimensional density function can be incorporated into the construction of Clenshaw-Curtis type quadrature rules, either through an adjustment of the quadrature weights or by generating a set of quadrature nodes that satisfies the optimal spacing property in terms of the density-weighted uniform error. We consider a variety of density functions, including those that are piecewise continuous, or have unbounded support. The accompanying numerical experiments illustrate the behavior and performance of the resulting quadrature rules and offer a comparison with a variety of existing approaches for estimating density weighted integrals.