Influence functions and efficiencies of the canonical correlation and canonical vectors estimates

Taskinen, Croux, Kankainen, Ollila & Oja (2006) — influence of canonical correlations

Result

influence functions of canonical correlations and vectors for general scatter-matrix functionals; for the sample covariance the squared correlation has $\operatorname{IF}(\rho_i^2)=2\rho_iu_iv_i-\rho_i^2(u_i^2+v_i^2)$ in the canonical variates $u_i,v_i$.

Use

the per-coefficient form whose average over $i$, divided by $\rho_i^2$, is O7.2's $\psi$; confirms the canonical-correlation check of the determinant-route influence function. Centred scatter and a random second block; O7 is uncentred with a fixed partition indicator.

Verification

formula seen through the citing restatement in arXiv:1705.04194 (Sinha et al. 2017) — the paper itself was not retrievable (AUDIT-RETENTION-PLUGIN-VECTOR, 6 Sep 2026).