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

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 CPCs 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.