Zhang Jingwen, Ibrahim Joseph, Li Tengfei, Zhu Hongtu
Department of Biostatistics, UNC Gillings School of Global Public Health, University of North Carolina at Chapel Hill.
Biomedical Research Imaging Center, UNC School of Medicine, University of North Carolina at Chapel Hill.
Proc AAAI Conf Artif Intell. 2019 Jan-Feb;33:5765-5772. doi: 10.1609/aaai.v33i01.33015765.
We consider the problem of performing an association test between functional data and scalar variables in a varying coefficient model setting. We propose a functional projection regression model and an associated global test statistic to aggregate relatively weak signals across the domain of functional data, while reducing the dimension. An optimal functional projection direction is selected to maximize signal-to-noise ratio with ridge penalty. Theoretically, we systematically study the asymptotic distribution of the global test statistic and provide a strategy to adaptively select the optimal tuning parameter. We use simulations to show that the proposed test outperforms all existing state-of-the-art methods in functional statistical inference. Finally, we apply the proposed testing method to the genome-wide association analysis of imaging genetic data in UK Biobank dataset.
我们考虑在变系数模型设定下，对函数型数据与标量变量进行关联检验的问题。我们提出了一种函数投影回归模型及相关的全局检验统计量，以在降低维度的同时，汇总函数型数据域上相对较弱的信号。通过岭罚则选择最优的函数投影方向，以最大化信噪比。理论上，我们系统地研究了全局检验统计量的渐近分布，并提供了一种自适应选择最优调谐参数的策略。我们通过模拟表明，所提出的检验在函数统计推断方面优于所有现有的先进方法。最后，我们将所提出的检验方法应用于英国生物银行数据集中影像遗传学数据的全基因组关联分析。
