2024-03-28T23:31:02Z
https://repository.dl.itc.u-tokyo.ac.jp/oai
oai:repository.dl.itc.u-tokyo.ac.jp:00042950
2022-12-19T04:18:02Z
62:7433:7434
9:7435:7436
Tail Probabilities of the Limiting Null Distributions of the Anderson-Stephens Statistics
Kuriki, Satoshi
98787
Takemura, Akimichi
98788
330
directional data
integral geometry
maximum of a Gaussian field
tivariate symmetric normal distribution
test for spherical uniformity
Weyl's formula
application/pdf
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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technical report
日本経済国際共同センター
2000-06
Discussion paper series. CIRJE-F
CF-77
AA11450569
eng
http://www.cirje.e.u-tokyo.ac.jp/research/dp/2000/2000cf77.pdf
http://doi.org/10.1016/S0047-259X(03)00093-9
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