A1157
Title: Numerical inversion of characteristic functions for exact multivariate statistical inference
Authors: Viktor Witkovsky - Slovak Academy of Sciences (Slovakia) [presenting]
Abstract: Computing the exact statistical distributions of multivariate test statistics is a challenging task. A method is proposed for calculating the distributions of multivariate test statistics based on the numerical inversion of the associated characteristic functions. These statistics are usually expressed as a linear combination or product of independent random variables with known distributions and characteristic functions. In addition, it is focused on the problem of inversion of multivariate characteristic functions. A numerical algorithm is proposed for the inversion of the bivariate characteristic function, and it is shown how it allows the use of complex probability distributions specified by the characteristic function, including the copula function. The problem of generating random numbers is also discussed when the bivariate distribution is specified by its characteristic function and an algorithm is proposed based on the conditional characteristic function. To illustrate the concept and application of these algorithms, a version of the bivariate logistic distribution specified is used by its characteristic function. The proposed method has been implemented in MATLAB's Characteristic Functions Toolbox (CharFunTool). The approach offers valuable insights into the challenges of inverting multivariate characteristic functions. It provides a promising approach for accurately and efficiently computing the exact statistical distributions in multivariate statistical analysis.
