Influence functions for certain parameters in multivariate analysis

Radhakrishnan & Kshirsagar (1981) — influence functions in multivariate analysis

Result

closed-form Hampel influence functions for the generalized variance, the regression-coefficient matrix, the MANOVA noncentrality matrix $\Sigma^{-1}\delta$ and its eigenvalues, canonical correlations, principal components and the parameters behind Pillai's statistic, Hotelling's $T_0^2$ and Wilks' $\Lambda$; $r^2$, $R^2$ and Mahalanobis $D^2$ as special cases.

Use

the matrix influence function named in O6.8 exists here in the centred several-populations form; at the evaluation law O7's $I_Z$ is the between-group matrix, so the study's $\psi$ must reduce to theirs.

Verification

abstract read (primary text, OpenAlex/T&F record); full text paywalled (5 Sep 2026 vector-study literature pass).