This article presents the first comprehensive studies on the local and global inferences for the smoothing spline estimate in a unified asymptotic framework. The novel functional Bahadur representation is developed as the theoretical foundation of this article, and is also of independent interest. Based on that, we establish four interconnected inference procedures: (i) Point-wise Confidence In...

The convergences of three L1 spline methods for scattered data interpolation and fitting using bivariate spline spaces are studied in this paper. That is, L1 interpolatory splines, splines of least absolute deviation, andL1 smoothing splines are shown to converge to the given data function under some conditions and hence, the surfaces from these three methods will resemble the given data values...

Let there be given error-contaminated measurements of function values at strictly ascending abscissae. We address the problem of calculating a best linear spline approximation to these data, whose knots are predefined on the abscissae. We establish conditions that allow the development of a special descent algorithm that takes into account the structure of the problem. 1 Index Terms data fittin...

A new package crs is introduced for computing nonparametric regression (and quantile) splines in the presence of both continuous and categorical predictors. B-splines are employed in the regression model for the continuous predictors and kernel weighting is employed for the categorical predictors. We also develop a simple R interface to NOMAD, which is a mixed integer optimization solver used t...

This paper extends spline methods to compact Riemannian manifolds in an rkhs setting. The approach is to use the mathematical framework of rkhs, along with integrating spectral geometry associated with compact Riemannian manifolds. This combination aarmatively answers a conjecture made by Wahba (1981) that spline interpolation and smoothing available for the 2{sphere can be generalized to compa...

Article history: Received 25 February 2011 Received in revised form 19 July 2011 Accepted 14 September 2011 Available online xxxx

This vignette outlines the implementation of the regression spline method contained in the R crs package, and also presents a few illustrative examples.

We study the convergence of discrete and penalized least squares spherical splines in spaces with stable local bases. We derive a bound for error in the approximation of a sufficiently smooth function by the discrete and penalized least squares splines. The error bound for the discrete least squares splines is explicitly dependent on the mesh size of the underlying triangulation. The error boun...

In this paper, a class of Bayesian hierarchical disease mapping models with spline smoothing are motivated and developed for sequential disease mapping and for surveillance of disease risk trends and clustering. The methodological development aims to provide reliable information about the patterns (both over space and time) of disease risk and to quantify uncertainty. Bayesian disease mapping m...