Multivariate saddlepoint tests on the mean direction of the von Mises-Fisher distribution
This article deals with the evaluation of the \(p\)-values of two tests on the parameters of the von Mises-Fisher distribution on directions. One test is a simultaneous test on the mean direction parameter vector and concentration parameter. The second is a conditional test on the mean direction with the concentration parameter known. Both tests make use of a test statistic based on the exponent of the saddle-point approximation to the density of multivariate \(M\)-estimators. The exponential form of the von Mises-Fisher distribution helps to reduce computational difficulties. The numerical minimization that is usually required for the saddle-point approximation is avoided here. Other saddle-point tests were used by others before, for the wrapped normal models, for a bootstrap variant of the wrapped normal model and for the von Mises-Fisher model also. The numerical accuracy of the tests is illustrated. A comparison with a Monte Carlo procedure shows that the relative errors are bounded. A brief introduction to saddle-point tests for the mean direction is also given.
scientific article; zbMATH DE number 6814692