Let X and Y be Banach spaces such that X has an unconditional basis. Then X Y, the injective tensor product of X and Y, has the Radon-Nikodym property （respectively, the analytic Radon-Nikodym property, the near Rad...Let X and Y be Banach spaces such that X has an unconditional basis. Then X Y, the injective tensor product of X and Y, has the Radon-Nikodym property （respectively, the analytic Radon-Nikodym property, the near Radon-Nikodym property, non-containment of a copy of co, weakly sequential completeness） if and only if both X and Y have the same property and each continuous linear operator from the predual of X to Y is compact.展开更多
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 ...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.展开更多
基金the National Natural Science Foundation of China,Grant No.10571035
文摘Let X and Y be Banach spaces such that X has an unconditional basis. Then X Y, the injective tensor product of X and Y, has the Radon-Nikodym property （respectively, the analytic Radon-Nikodym property, the near Radon-Nikodym property, non-containment of a copy of co, weakly sequential completeness） if and only if both X and Y have the same property and each continuous linear operator from the predual of X to Y is compact.
文摘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.
