Significance testing for canonical correlation analysis in high dimensions
针对高维数据中两组变量间线性关系的检验问题，提出一种基于选择后推断的稳定一步估计量，并开发了贪心搜索算法，用于检验预设基数的子集间是否存在线性关系。
We consider the problem of testing for the presence of linear relationships between large sets of random variables based on a post-selection inference approach to canonical correlation analysis. The challenge is to adjust for the selection of subsets of variables having linear combinations with maximal sample correlation. To this end, we construct a stabilized one-step estimator of the euclidean-norm of the canonical correlations maximized over subsets of variables of pre-specified cardinality. This estimator is shown to be consistent for its target parameter and asymptotically normal, provided the dimensions of the variables do not grow too quickly with sample size. We also develop a greedy search algorithm to accurately compute the estimator, leading to a computationally tractable omnibus test for the global null hypothesis that there are no linear relationships between any subsets of variables having the pre-specified cardinality. We further develop a confidence interval that takes the variable selection into account.