Influence functions of two families of robust estimators under proportional scatter matrices

In this paper, under a proportional model, two families of robust estimates for the proportionality constants, the common principal axes and their size are discussed. The first approach is obtained by plugging robust scatter matrices on the maximum likelihood equations for normal data. A projection- pursuit and a modified projection-pursuit approach, adapted to the proportional setting, are also considered. For all families of estimates, partial influence functions are obtained and asymptotic variances are derived from them. The performance of the estimates is compared through a Monte Carlo study. © 2006 Springer-Verlag.