A new projection-based definition of quantiles in a multivariate setting is proposed. This approach extends in a natural way to infinite-dimensional Hilbert spaces. The directional quantiles we define are shown to satisfy desirable properties of equivariance and, from an interpretation point of...

A general depth measure, based on the use of one-dimensional linear continuous projections, is proposed. The applicability of this idea in different statistical setups (including inference in functional data analysis, image analysis and classification) is discussed. A special emphasis is made on...

In this paper we propose nonparametric estimates of the regression function and its derivative when it is only assumed a weak error's structure. We study their local and global asymptotic behaviour when we observe dependent trajectories.

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.

We consider a problem of nonparametric density estimation under shape restrictions. We deal with the case where the density belongs to a class of Lipschitz functions. Devroye [L. Devroye, A Course in Density Estimation, in: Progress in Probability and Statistics, vol. 14, Birkhuser Boston Inc.,...

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...