Testing for spherical and elliptical symmetry
Journal of Multivariate Analysis(2020)
摘要
We construct new testing procedures for spherical and elliptical symmetry based on the characterization that a random vector X with finite mean has a spherical distribution if and only if E[u⊤X|v⊤X]=0 holds for any two perpendicular vectors u and v. Our test is based on the Kolmogorov–Smirnov statistic, and its rejection region is found via the spherically symmetric bootstrap. We show the consistency of the spherically symmetric bootstrap test using a general Donsker theorem which is of some independent interest. For the case of testing for elliptical symmetry, the Kolmogorov–Smirnov statistic has an asymptotic drift term due to the estimated location and scale parameters. Therefore, an additional standardization is required in the bootstrap procedure. In a simulation study, the size and the power properties of our tests are assessed for several distributions and the performance is compared to that of several competing procedures.
更多查看译文
关键词
primary,secondary
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络