Multivariate saddlepoint tests on the mean direction of the von Mises–Fisher distribution

R. Gatto ()
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R. Gatto: University of Bern

Metrika: International Journal for Theoretical and Applied Statistics, 2017, vol. 80, issue 6, No 8, 733-747

Abstract: Abstract This article provides P values for two new tests on the mean direction of the von Mises–Fisher distribution. The test statistics are obtained from the exponent of the saddlepoint approximation to the density of M-estimators, as suggested by Robinson et al. (Ann Stat 31:1154–1169, 2003). These test statistics are chi-square distributed with asymptotically small relative errors. Despite the high dimensionality of the problem, the proposed P values are accurate and simple to compute. The numerical precision of the P values of the new tests is illustrated by some simulation studies.

Keywords: Cumulant generating function; Directional distribution; M-functional; Minimum $$L_2$$ L 2 -distance estimator; P value; Relative error; 62F03 Hypothesis testing, 62H11 Directional data; spatial statistics (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s00184-017-0625-0

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