Graciela Boente

Robust principal component analysis for functional data

A method for exploring the structure of populations of complex objects, such as images, is considered. The objects are summarized by feature vectors. The statistical backbone is Principal Component Analysis in the space of feature vectors. Visual insights come from representing the results in the original data space. In an ophthalmological example, endemic outliers motivate the development of a bounded influence approach to PCA.

Kernel-based functional principal components (

In this paper, we propose kernel-based smooth estimates of the functional principal components when data are continuous trajectories of stochastic processes. Strong consistency and the asymptotic distribution are derived under mild conditions.

ROBUST FUNCTIONAL PRINCIPAL COMPONENTS: A PROJECTION-PURSUIT APPROACH

In many situations, data are recorded over a period of time and may be regarded as realizations of a stochastic process. In this paper, robust estimators for the principal components are considered by adapting the projection pursuit approach to the functional data setting. Our approach combines robust projection-pursuit with different smoothing methods. Consistency of the estimators are shown under mild assumptions. The performance of the classical and robust procedures are compared in a simulation study under different contamination schemes. 1. Introduction. Analogous to classical principal components analysis (PCA), the projection-pursuit approach to robust PCA is based on finding projections of the data which have maximal dispersion. Instead of using the variance as a measure of dispersion, a robust scale estimator sn is used for the maximization problem. This approach was introduced by Li and Chen (1985), who proposed estimators based on maximizing (or minimizing) a robust scale. In this way, given a sample xi ∈ R d ,1 ≤ i ≤ n, the first robust principal component vector is defined as

Consistency of a nonparametric estimate of a density function for dependent variables

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.

Robust plug-in bandwidth estimators in nonparametric regression

Abstract In this paper, we propose a robust bandwidth selection method for local M-estimates used in nonparametric regression. We study the asymptotic behavior of the resulting estimates. We use the results of a Monte Carlo study to compare the performance of various competitors for moderate samples sizes. It appears that the robust plug-in bandwidth selector we propose compares favorably to its competitors, despite the need to select a pilot bandwidth. The Monte Carlo study shows that the robust plug-in bandwidth selector is very stable and relatively insensitive to the choice of the pilot.

A Robust Approach to Common Principal Components

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.

Strong uniform convergence rates for some robust equivariant nonparametric regression estimates for mixing processes

Summary In this paper we prove the strong uniform consistency of some robust equivariant nonparametric regression estimates, based on kernel weights and on nearest neighbor with kernel weights, for strongly and uniform strongly mixing processes. Strong uniform convergence rates for these estimates are obtained. Applications to robust nonparametric autoregression are given.

Sorption isotherms of corn—Study of mathematical models

In this paper statistical methodology is used to determine similar groups of Argentine maize varieties and to model the behaviour of the moisture content as a function of the water activity. Different equations proposed in the literature are studied and a common mathematical model is obtained for all varieties whatever the adequacy criteria considered. The use of the goodness of fit criteria is also discussed.

Robust Estimators under Semi-Parametric Partly Linear Autoregression: Asymptotic Behaviour and Bandwidth Selection

In this article, under a semi-parametric partly linear autoregression model, a family of robust estimators for the autoregression parameter and the autoregression function is studied. The proposed estimators are based on a three-step procedure, in which robust regression estimators and robust smoothing techniques are combined. Asymptotic results on the autoregression estimators are derived. Besides combining robust procedures with M-smoothers, predicted values for the series and detection residuals, which allow to detect anomalous data, are introduced. Robust cross-validation methods to select the smoothing parameter are presented as an alternative to the classical ones, which are sensitive to outlying observations. A Monte Carlo study is conducted to compare the performance of the proposed criteria. Finally, the asymptotic distribution of the autoregression parameter estimator is stated uniformly over the smoothing parameter. Copyright 2007 The Authors Journal compilation 2007 Blackwell Publishing Ltd.

S -Estimators for Functional Principal Component Analysis

Principal component analysis is a widely used technique that provides an optimal lower-dimensional approximation to multivariate or functional datasets. These approximations can be very useful in identifying potential outliers among high-dimensional or functional observations. In this article, we propose a new class of estimators for principal components based on robust scale estimators. For a fixed dimension q, we robustly estimate the q-dimensional linear space that provides the best prediction for the data, in the sense of minimizing the sum of robust scale estimators of the coordinates of the residuals. We also study an extension to the infinite-dimensional case. Our method is consistent for elliptical random vectors, and is Fisher consistent for elliptically distributed random elements on arbitrary Hilbert spaces. Numerical experiments show that our proposal is highly competitive when compared with other methods. We illustrate our approach on a real dataset, where the robust estimator discovers atypical observations that would have been missed otherwise. Supplementary materials for this article are available online.