Sparse canonical correlation analysis between an alcohol biomarker and self-reported alcohol consumption. (English) Zbl 06837398

Helian, Shanjun; Brumback, Babette A.; Cook, Robert L.

Commun. Stat., Simulation Comput. 46, No. 10, 7924-7941 (2017).

Summary: In investigating the correlation between an alcohol biomarker and self-report, we developed a method to estimate the canonical correlation between two high-dimensional random vectors with a small sample size. In reviewing the relevant literature, we found that our method is somewhat similar to an existing method, but that the existing method has been criticized as lacking theoretical grounding in comparison with an alternative approach. We provide theoretical and empirical grounding for our method, and we customize it for our application to produce a novel method, which selects linear combinations that are step functions with a sparse number of steps.

MSC:

62H20	Measures of association (correlation, canonical correlation, etc.)
62G08	Nonparametric regression and quantile regression

Keywords:

\(L^1\) penalty; partial canonical correlation; regularized canonical correlation analysis; repeated measures