Journal of Statistical Planning and Inference ( IF 0.9 ) Pub Date : 2021-08-21 , DOI: 10.1016/j.jspi.2021.08.002 Fanrong Zhao 1 , Nan Lin 2 , Wenjuan Hu 1 , Baoxue Zhang 1
Testing the dependence between the response and the functional predictor in a functional linear model is of fundamental importance. In this paper, based on a U-statistic of order two, we develop a computationally more efficient test for lacking of dependence in functional linear regression model. By the martingale central limit theorem, we prove that the asymptotic normality of the proposed test statistic under some mild regularity conditions. Simulation results show that our proposed test can be tens or hundreds time faster than the FLUTE test by Hu et al. (2020) which uses a U-statistic of order four. We further demonstrate the superiority of our test by two real data applications.
中文翻译:
用于测试函数线性模型独立性的更快 U 统计量
在函数线性模型中测试响应与函数预测器之间的相关性至关重要。在本文中,基于二阶 U 统计量,我们开发了一种计算上更有效的测试,用于在函数线性回归模型中缺乏依赖性。通过鞅中心极限定理,我们证明了所提出的检验统计量在一些温和的正则性条件下的渐近正态性。仿真结果表明,我们提出的测试可以比 Hu 等人的 FLUTE 测试快数十或数百倍。(2020) 使用四阶 U 统计量。我们通过两个真实的数据应用程序进一步证明了我们测试的优越性。