Multivariate saddlepoint tests on the mean direction of the von Mises-Fisher distribution
type: Item
instance of: scholarly article
title: Multivariate saddlepoint tests on the mean direction of the von Mises-Fisher distribution
zbMATH Open document ID: 1392.62054
author: Peng Zhang
published in: Metrika
publication date: 2017-12-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62F03
Mathematics Subject Classification ID: 62H11
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 6814692
zbMATH Keywords: statistical tests
zbMATH Keywords: \(p\)-values
zbMATH Keywords: von Mises-Fisher distribution
zbMATH Keywords: saddle-point approximation
zbMATH Keywords: \(M\)-estimators
reviewed by: Arakaparampil M. Mathai
MaRDI profile type: Publication
full work available at URL: s00184-017-0625-0
OpenAlex ID: W2755034157
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DOI: 10.1007/S00184-017-0625-0
description: scientific article; zbMATH DE number 6814692