CONSISTENCY OF RIDGE FUNCTION FIELDS FOR VARYING NONPARAMETRIC REGRESSION

Robert Frouin (1) , Bruno Pelletier (2)

1 SIO - UC San Diego - Scripps Institution of Oceanography
2 IRMAR - Institut de Recherche Mathématique de Rennes

A nonparametric regression model proposed in [Pelletier and Frouin, Ap- plied Optics, 2006] as a solution to the geophysical problem of ocean color remote sensing is studied. The model, called ridge function field, com- bines a regression estimate in the form of a superposition of ridge func- tions, or equivalently a neural network, with the idea pertaining to varying- coefficients models, where the parameters of a parametric family are allowed to vary with other variables. Under mild assumptions on the underlying dis- tribution of the data, the strong universal consistency of the least-squares ridge function fields estimate is established.

Mots clés: Varying coefficients model; ridge function approximation; nonparametric regression; universal consistency; least squares.; least squares

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Robert Frouin, Bruno Pelletier. CONSISTENCY OF RIDGE FUNCTION FIELDS FOR VARYING NONPARAMETRIC REGRESSION. Communications in Statistics - Theory and Methods, 2009, 38 (8), pp.1272-1283. ⟨10.1080/03610920802395702⟩. ⟨hal-00460632⟩