On some characterizations and multidimensional criteria for testing homogeneity, symmetry and independencel

JOURNAL OF MULTIVARIATE ANALYSIS

卷:173

Article

Chen, Feifei¹  Meintanis, Simos G.^2,3  Zhu, Lixing^3,4 

[1] Renmin Univ China, Sch Stat, Beijing, Peoples R China

[2] Univ Athens, Dept Econ, Athens, Greece

[3] North West Univ, Unit Business Math & Informat, Potchefstroom, South Africa

[4] Hong Kong Baptist Univ, Dept Math, Hong Kong, Peoples R China

关键词: Characteristic function;    Distance correlation;    Independence testing;    Symmetry testing;    Two-sample problem;   

DOI  :  10.1016/j.jmva.2019.02.006

来源: Elsevier

【 摘 要 】

We propose three new characterizations and corresponding distance-based weighted test criteria for the two-sample problem, and for testing symmetry and independence with multivariate data. All quantities have the common feature of involving characteristic functions, and it is seen that these quantities are intimately related to some earlier methods, thereby generalizing them. The connection rests on a special choice of the weight function involved. Equivalent expressions of the distances in terms of densities are given as well as a Bayesian interpretation of the weight function is involved. The asymptotic behavior of the tests is investigated both under the null hypothesis and under alternatives, and affine invariant versions of the test criteria are suggested. Numerical studies are conducted to examine the performances of the criteria. It is shown that the normal weight function, which is the hitherto most often used, is seriously suboptimal. The procedures are biased in the sense that the corresponding test criteria degenerate in high dimension and hence a bias correction is required as the dimension tends to infinity. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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