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

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  • R. Gatto

    (University of Bern)

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.

Suggested Citation

  • R. Gatto, 2017. "Multivariate saddlepoint tests on the mean direction of the von Mises–Fisher distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 733-747, November.
    • Handle: RePEc:spr:metrik:v:80:y:2017:i:6:d:10.1007_s00184-017-0625-0
    DOI: 10.1007/s00184-017-0625-0
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    References listed on IDEAS

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    1. Ma, Yanyuan & Ronchetti, Elvezio, 2011. "Saddlepoint Test in Measurement Error Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 147-156.
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