Abstract:

CCA is a classical tool to study the relationship between two sets of variables. We will discuss two closely related problems in high-dimensional CCA: sparse estimation of the directions and significance testing of the correlation.

In the first part, we discuss a new sparse CCA (SCCA) method that recasts high-dimensional CCA as an iterative penalized least squares problem. The new iterative penalized least squares formulation leads to a direct penalized estimation approach to the sparse CCA problem and efficient algorithms. In contrast to some existing methods, the new SCCA does not impose any sparsity assumptions on the covariance matrices and can consistently estimate the true CCA directions with an overwhelming probability in ultra-high dimensions. This part of the talk is based on joint work with Qing Mai.

In the second part, we discuss the problem of testing for the presence of linear relationships between large sets of random variables based on a post-selection inference approach to CCA. 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 square-root of Pillai's trace 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. This part of the talk is based on joint work with Ian McKeague.

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Topic: Colloquia: Department of Statistics and Actuarial Science, The University of Iowa

Time: Nov 19, 2020 03:15 PM Central Time (US and Canada)

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Meeting ID: 970 2130 9544