Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Assistant Prof. Hans-Werner van Wyk，Mathematics & Statistics, Auburn University, USA
Inviter:	龚伟副研究员
Title:	Clenshaw-Curtis Type Rules for Statistical Integrals
Time & Venue:	2019.7.2 15:00-16:00 Z301
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.