Estimation of canonical correlation directions: From Gaussian to sub-Gaussian population

Youming Liu and Chunguang Ren

Journal of Multivariate Analysis, 2021, vol. 186, issue C

Abstract: Cai and Zhang (2018) established separate perturbation upper bound estimators for canonical correlation directions under centered Gaussian population and some conditions on the minimum singular value σr(S) of a correlation matrix S . They posed an open problem for the optimality of their estimators. In this paper, the optimality of Cai and Zhang’s estimation is firstly proved up to some multiplicated constants. Then motivated by Ma and Li’s work (Ma and Li, 2020), we give an upper bound estimation for centered sub-Gaussian population, and a better estimate for bounded sub-Gaussian population. Finally, all estimates are extended from centered population to non-centered one.

Keywords: Canonical correlation directions; Gaussian and sub-Gaussian population; Optimal estimation; sinΘ distance; Singular value decomposition (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.jmva.2021.104795

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