Convergence rates for multivariate smoothing spline functions

Convergence Rates for Smoothing Spline Estimators in Varying Coefficient Models

We consider the estimation of a multiple regression model in which the coefficients change slowly in “time”, with “time” being an additional covariate. Under reasonable smoothness conditions, we prove the usual expected mean square error bounds for the smoothing spline estimators of the coefficient functions.

Smoothing by Spline Functions

On Smooth Multivariate Spline Functions

In this paper the dimensions of bivariate spline spaces with simple cross-cut grid partitions are determined and expressions of their basis functions are given. Consequently, the closures of these spaces over all partitions of the same type can be determined. A somewhat more detailed study on bivariate splines with rectangular grid partitions is included. The results in this paper can be applie...

Smoothing Noisy Data with Spline Functions *

I t is shown how to choose the smoothing parameter when a smoothing periodic spline of degree 2m -1 is used to reconstruct a smooth periodic curve from noisy ordinate data. The noise is assumed "white" , and the true curve is assumed to be in the Sobolev space W,(*ra) of periodic functions with absolutely continuous v-th derivative, v = 0, t . . . . . 2 m I and square integrable 2m-th derivativ...

Smoothing Spline Estimation of Variance Functions

This article considers spline smoothing of variance functions. We focus on selection of smoothing parameters and develop three direct data-driven methods: unbiased risk (UBR), generalized approximate cross validation (GACV) and generalized maximum likelihood (GML). In addition to guaranteed convergence, simulations show that these direct methods perform better than existing indirect UBR, genera...