Computational Mathematics and Statistics Seminar by Pingan He: Representative Points of Meta Distributions and Their Applications
Speaker: , Ph.D. candidate, Beijing Normal-Hong Kong Baptist University
Title: Representative Points of Meta Distributions and Their Applications
Abstract: Modeling multivariate dependence via copulas is central to modern risk analysis and compositional data modeling. Practical inference typically relies on Monte Carlo or quasi–Monte Carlo sampling, whose efficiency can deteriorate under nonlinear marginal transformations and in moderate dimensions. We develop a mean squared error–based representative point (MSE-RP) framework for meta Gaussian, meta t, and Dirichlet copula models. Our method integrates number-theoretic lattice constructions with stochastic representations of elliptical distributions to produce stable and low-bias discrete approximations. We also establish structural results for covariance, conditional moments, and tail behavior, including extreme-value limits for Dirichlet copulas. Simulation studies in dimensions two to four show that MSE-RPs substantially reduce bias in moment and dependence estimation compared to MC and QMC methods, particularly in small samples. Applications to portfolio risk demonstrate improved estimation of Value-at-Risk and Expected Shortfall, highlighting both statistical and computational efficiency gains.
Computational Mathematics and Statistics Seminar