Robustness and efficiency of the residual scale estimators in the regression model is important for robust inference. We introduce the class of robust generalized M-scale estimators for the regression model, derive their influence function and gross-error sensitivity, and study their maxbias...

In the finite-dimensional setting, Li and Chen (1985) proposed a method for principal components analysis using projection-pursuit techniques. This procedure was generalized to the functional setting by Bali et al. (2011), where also different penalized estimators were defined to provide smooth...

As in the multivariate setting, the class of elliptical distributions on separable Hilbert spaces serves as an important vehicle and reference point for the development and evaluation of robust methods in functional data analysis. In this paper, we present a simple characterization of elliptical...

The asymptotic distribution of the eigenvalues and eigenvectors of the robust scatter matrix proposed by R. Maronna in 1976 is given when the observations are from an ellipsoidal distribution. The elements of each characteristic vector are the coefficients of a robustified version of principal...

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...

In many situations, when dealing with several populations with different covariance operators, equality of the operators is assumed. Usually, if this assumption does not hold, one estimates the covariance operator of each group separately, which leads to a large number of parameters. As in the...

In this paper strong consistency and uniform complete consistency of the nonparametric density estimator proposed by [5], 1049-1051) is proved for [phi]-mixing and [alpha]-mixing processes.

In this paper, we propose a new family of density estimates closely related to the nearest neighbor estimates introduced by Loftsgaarden and Quesenberry. An optimal estimator, wit respect to the asymptotic mean square error, is obtained for a given distribution.

Under normality, Flury and Schmid [Quadratic discriminant functions with constraints on the covariances matrices: some asymptotic results, J. Multivariate Anal. 40 (1992) 244-261] investigated the asymptotic properties of the quadratic discrimination procedure under hierarchical models for the...

In this paper we define a robust conditional location functional without requiring any moment condition. We apply the nonparametric proposals considered by C. Stone (Ann. Statist. 5 (1977), 595-645) to this functional equation in order to obtain strongly consistent, robust nonparametric...