Consistency of Ridge Function Fields for Varying Nonparametric Regression
A nonparametric regression model proposed in Pelletier and Frouin (2006) as a solution to the geophysical problem of ocean color remote sensing is studied. The model, called ridge function field, combines a regression estimate in the form of a superposition of ridge functions, or which is equivalent to 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 distribution of the data, the strong universal consistency of the least-squares ridge function fields estimate is established.