Fisher information for a multivariate extreme value distribution

Explicit algebraic formulae for the Fisher information matrixof the multivariate extreme value distribution with generalisedextreme value margins and logistic dependence structure aregiven.     

Applications and Tabulations of the Multivariate t Distribution with ρ = 0

Quantiles of the multivariate t distribution with ρ = 0 are tabulated. Some applications are discussed.     

One‐sided Simultaneous Confidence Intervals for Effective Dose Steps in Unbalanced Designs

An important issue in dose finding is whether a further dose increment leads to a relevant increase in efficacy. Clinical efficacy should not be considered by point zero null hypotheses. Instead, shifted hypotheses for the difference or the ratio can be used. Because the a priori definition of a relevance threshold is frequently difficult, confidence intervals should be used for a posteriori interpretation. Sample size estimation – a‐priori or by adaptive interim analysis‐ is inherent, because the effective dose steps are arbitrary in un‐designed studies. For simultaneous confidence intervals without order restriction the exact distributions under the null and the alternative hypothesis is proposed for the general unbalanced one‐way design.     

On the Numerical Availability of Multiple Comparison Procedures

In the past many multiple comparison procedure were difficult to perform. Usually, such procedures can be traced back to studentized multiple contrast tests. Numerical difficulties restricted the use of the exact procedures to simple, commonly balanced, designs. Conservative approximations or simulation based approaches have been used in the general cases. However, new efforts and results in the past few years have led to fast and efficient computations of the underlying multidimensional integrals. Inferences for any finite set of linear functions of normal means are now numerically feasible. These include all‐pairwise comparisons, comparisons with a control (including dose‐response contrasts), multiple comparison with the best, etc. The article applies the numerical progress on multiple comparisons procedures for common balanced and unbalanced designs within the general linear model.