Omnibus Model Checks of Linear Assumptions through Distance Covariance
Omnibus Model Checks of Linear Assumptions through Distance Covariance
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DOI：
10.5705/ss.202019.0311
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发表时间：
2021
影响因子：
1.4
通讯作者：
Kai Xu;Daojiang He
中科院分区：
文献类型：
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作者：
Kai Xu;Daojiang He
统计学文献中有大量关于检验线性是否充分的研究，但从关联性度量的角度开展的研究却极为有限。受著名的距离协方差（塞克利、里佐和巴基罗夫，2007年，dCov）启发，我们提出了两种用于检验线性拟合优度的综合性检验方法。从方法学角度而言，我们的检验不涉及任何调谐参数，实施起来十分便捷。从理论层面看，由于dCov所诱导的核函数并不平滑，相关技术细节具有独立的研究价值。我们研究了在原假设、固定备择假设和局部备择假设下我们所提检验方法的收敛性，并设计了一种自助法来近似其原分布，同时证明了该方法的一致性。通过数值研究，将我们提出的方法与一些现有方法进行比较，以展示其有效性。
An enormous amount of research performed on checking the adequacy of linearity are available in the statistical literature, but there exists very limited amount of work from the viewpoint of a measure of association. Inspired by the well-known distance covariance (Székely, Rizzo and Bakirov, 2007, dCov), we propose two omnibus tests for the goodness-of-fit of linearity. Methodologically, our tests do not involve any tuning parameters and are conveniently implemented. Theoretically, the technical details are of independent interest mainly due to the fact that the kernel induced by the dCov is not smooth. Convergence of our tests under null, fixed and local alternative hypotheses is investigated, and a bootstrap scheme is devised to approximate their null distributions and its consistency is justified. Numerical studies are employed to demonstrate the effectiveness of our proposals in comparison with some existing counterparts.