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Tail probabilities of the limiting null distributions of the Anderson-Stephens statistics

Listed author(s):
  • Satoshi Kuriki

    (The Institute of Statistical Mathematics)

  • Akimichi Takemura

    (Faculty of Economics, University of Tokyo)

Registered author(s):

    For the purpose of testing the spherical uniformity based on i.i.d. directional data (unit vectors) zi, i =1,...,n, Anderson and Stephens (1972) proposed testing procedures based on the statistics Smax = maxuS (u) and S min = minuS (u), where u is a unit vector and nS (u) is the sum of square of u'zi's. In this paper we also consider another test statistic Srange = Smax -Smin. We provide formulas for the P-values of Smax , Smin , Srange by approximating tail probabilities of the limiting null distributions by means of the tube method, an integral-geometric approach for evaluating tail probability of the maximum of a Gaussian random field. Monte Carlo simulations for examining the accuracy of the approximation and for the power comparison of the statistics are given.

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    Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-77.

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    Length: 32 pages
    Date of creation: Jun 2000
    Handle: RePEc:tky:fseres:2000cf77
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