Tail Probabilities of the Limiting Null Distributions of the Anderson-Stephens Statistics
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アイテムタイプ
テクニカルレポート / Technical Report
言語
英語
キーワード
directional data, integral geometry, maximum of a Gaussian field, tivariate symmetric normal distribution, test for spherical uniformity, Weyl's formula
Institute of Statistical Mathematics
University of Tokyo
抄録
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.
内容記述
本文フィルはリンク先を参照のこと
雑誌名
Discussion paper series. CIRJE-F
巻
CF-77
発行年
2000-06
書誌レコードID
AA11450569
フォーマット
application/pdf
日本十進分類法
330
出版者
日本経済国際共同センター
出版者別名
Center for International Research on the Japanese Economy
Tail Probabilities of the Limiting Null Distributions of the Anderson-Stephens Statistics
