The multivariate resistant regression spline (MURRS) method for estimatingan underlying smooth J-variate function by using noisy data is based on approximatingit with tensor products of B-splines and minimizing a sum of the ρ-functions of the residuals to obtain a robust estimator of the regression function, where the spline knots areautomatically chosen through a parallel of information criterion. When the knots are deterministically given, it is proved that the MURRS estimator achieves the optimal globalconvergence rates established by Stone under some mild conditions. Examples are givento illustrate the utility of the proposed methodology. Usually, only a few tensor productsof B-splines are enough to fit even complicated functions.

The multivariate resistant regression spline (MURRS) method for estimatingan underlying smooth J-variate function by using noisy data is based on approximatingit with tensor products of B-splines and minimizing a sum of the ρ-functions of the residuals to obtain a robust estimator of the regression function, where the spline knots areautomatically chosen through a parallel of information criterion. When the knots are deterministically given, it is proved that the MURRS estimator achieves the optimal globalconvergence rates established by Stone under some mild conditions. Examples are givento illustrate the utility of the proposed methodology. Usually, only a few tensor productsof B-splines are enough to fit even complicated functions.