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Some blum-kiefer-rosenblatt type tests for the joint independence of variables
Authors:Ping Jing  Li-Xing Zhu
Affiliation:1. Graduate School of Science and Technology Chiba University , Chiba, 263, Japan;2. Institute of Applied Mathematics , Chinese Academy of Sciences , Beijing, 100080, China
Abstract:Testing the joint independence of variables has long been an interesting issue in statistical inferences. Blum, Kiefer and Rosenblatt (1961) suggested a test based on a sample distribution function. To overcome the sparseness of data points in high-dimensional space and deal with general cases, we in this paper suggest several extended versions of B-K-R tests via projection pursuit. Bootstrap method is applied to determine the critical values and for computational reason, an approximation derived by Number-theoretic method, for the bootstrap statistics is suggested. Several simulation experiments are performed and a real-life example is investigated.
Keywords:bootstrap method  number-theoretic method  projection pursuit type statistic  test of independence
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