A robust approach to common principal components

BOENTE, GRACIELA; ORELLANA, LILIANA

Statistics in Genetics and in the Environmental Sciences

Birkhauser

Lugar: Basel-Boston-Berlin; Año: 2001; p. 117 - 147

The common principal component model for several groups of multivariate observations assumes equal principal component axes but different variances along these axes in the groups. Two families of robust estimates for this model are introduced and discussed. The first approach is based on replacing the sample covariance matrices of each population by robust scatter matrices in the likelihood equations or by considering the pooled matrix, while the second one is based on projection--pursuit. For the first approach, the asymptotic distribution of the common principal axes estimates is established. Also, the asymptotic behavior of the eigenvalue estimates is derived by requiring the eigenvector estimates to be root--n consistent. For the projection--pursuit estimates, an algorithm, similar to that given for the one--population setting, is proposed. Maximum biases in neighborhoods of a normal distribution are derived under mild conditions. Through a Monte Carlo study the performance of the estimates is compared.