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General projection--pursuit estimators for common principal components model: Influence functions and Monte Carlo study.

Boente, Graciela; Pires, Ana M.; Rodrigues, Isabel M.

Journal of Multivariate Analysis, 97 (2006), 124-147

The common principal components (CPC) model for several groups of multivariate observations
assumes equal principal axes but possibly different variances along these axes among the groups.
Under a CPC model, generalized projection-pursuit estimators are defined by using score functions
on the dispersion measure considered. Their partial influence functions are obtained and asymptotic
variances are derived from them. When the score function is taken equal to the logarithm, it is shown
that, under a proportionality model, the eigenvector estimators are optimal in the sense of minimizing
the asymptotic variance of the eigenvectors, for a given scale measure.