Robust estimators under a functional partial linear model

BOENTE, GRACIELA; SALIBIAN-BARRERA, MATÍAS; VENA, PABLO

Londres

Conferencia; X International Conference of the ERCIMWorking Group on Computing & Statistics (ERCIM2017); 2017

University of London, Brikbeck University of London

Functional data analysis provides modern analytical tools for data that are recoded as images or as a continuous phenomenon over a period oftime. Because of the intrinsic nature of these data, they can be viewed as realizations of random functions often assumed to be in a Hilbert spacesuch as L2(I), with I a real interval or a finite dimensional Euclidean set. Partial linear modelling ideas have recently been adapted to situations in which functional data are observed. More precisely, two generalizations have been considered to deal with the problem of predicting a real valued response variable using explanatory variables that include a functional element, usually a random function, and a random variable. The semi-functional partial linear regression model allows the functional explanatory variables to act in a free nonparametric manner, while the scalar covariate corresponds to the linear component. On the other hand, the so-called functional partial linear model assumes that the scalar response is explained by a linear operator of a random function and a nonparametric function of a real?valued random variable. We will briefly discuss some approaches leading to obtain robust estimators functional partial linear model.