Finding Critical Values using Numerical Integration

Keywords: critical value, confindence interval, multivariate integration

Abstract: The problem of finding critical values for multivariate distributions is discussed and analyzed. The solution for this problem requires the combination of a numerical optimization method with a numerical integration method. Key issues are a) how to balance the error from the optimization method with the estimated error from the numerical integration method, and b) how to make efficient use of time consuming numerical integration computations for multivariate distributions. An algorithm for the problem will be described. The use of the algorithm will be illustrated with examples that use multivariate normal and multivariate t distributions.