Approximations to multivariate $t$ integrals with application to multiple comparison procedures

Alan Genz
Department of Mathematics
Washington State University
Pullman, WA USA
- Frank Bretz
Research Unit Bioinformatics
University of Hannover
Hannover, Germany
- Yosef Hochberg
Department of Statistics and Operations Research
School of Mathematical Sciences
Tel Aviv University, Israel

Abstract:

Various multiple comparison procedures involve the evaluation of multivariate normal and $t$ integrals with non-decomposable correlation matrices. While exact methods exist for their computations, it is sometimes necessary to consider simpler and faster approximations. We consider approximations based on approximations to the correlation matrix (methods which provide no error control) as well as inequality based methods (where, by definition, the sign of the error is known). Comparisons of different methods, in order to assess their accuracy, are given for particular multiple comparison problems which require high-dimensional integrations.