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

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  • Liu, Youming
  • Ren, Chunguang

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.

Suggested Citation

  • Liu, Youming & Ren, Chunguang, 2021. "Estimation of canonical correlation directions: From Gaussian to sub-Gaussian population," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:jmvana:v:186:y:2021:i:c:s0047259x21000737
    DOI: 10.1016/j.jmva.2021.104795
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