Simultaneous confidence intervals from randomization tests with application in testing bioequivalence with multiple endpoints

We propose a method to construct simultaneous confidence intervals for a parameter vector from inverting a series of randomization tests (RT). The randomization tests are facilitated by an efficient multivariate Robbins–Monro procedure that takes the correlation information of all components into account. The estimation method does not require any distributional assumption of the population other than the existence of the second moments. The resulting simultaneous confidence intervals are not necessarily symmetric about the point estimate of the parameter vector but possess the property of equal tails in all dimensions. In particular, we present the constructing the mean vector of one population and the difference between two mean vectors of two populations. Extensive simulation is conducted to show numerical comparison with four methods. We illustrate the application of the proposed method to test bioequivalence with multiple endpoints on some real data.