Deriving and Applying Improved Upper Bounds for Multivariate Normal Probability Outside of N-Cubes

摘要

Two related improved Bonferroni methods to obtain upper bounds for the probabilities of unions of events are described. One procedure (bivariate method) uses probabilities of events and pairwise intersections of events. The other superior and more complicated procedure (trivariate method) uses probabilities of pairwise and three way intersections of events. These new methods are applied to multivariate normal hypothesis testing and simultaneous unbiased confidence intervals and are shown to give results superior to those of the currently used procedure (conservative assumption and independence of events) if the number of variables is not too large and the data is highly correlated. Modifications of these new methods to non-normal probabilities and different types of probability regions are also mentioned. Keywords: Statistical processes. (kr)