There are two popular smoothing parameter selection methods for spline smoothing. First, smoothing parameters can be estimated minimizing criteria that approximate the average mean squared error of the regression function estimator. Second, the maximum likelihood paradigm can be employed, under the assumption that the regression function is a realization of some stochastic process. In this arti...

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...

In this paper, we propose control theoretic smoothing splines with L optimality for reducing the number of parameters that describes the fitted curve as well as removing outlier data. A control theoretic spline is a smoothing spline that is generated as an output of a given linear dynamical system. Conventional design requires exactly the same number of base functions as given data, and the res...

In the study of smoothing spline estimators, some convolution-kernellike properties of the Green’s function for an appropriate boundary value problem, depending on the design density, are needed. For the uniform density, the Green’s function can be computed more or less explicitly. Then, integral equation methods are brought to bear to establish the kernel-like properties of said Green’s functi...

Constrained smoothing splines are discussed under order restrictions on the shape of the function m. We consider shape constraints of the type m> 0, i.e. positivity, monotonicity, convexity, . . .. (Here for an integer r > 0, m denotes the rth derivative of m.) The paper contains three results: (1) constrained smoothing splines achieve optimal rates in shape restricted Sobolev classes; (2) they...

An algorithm is presented for constructing smoothing splines on the torus. The algorithm uses a particular representation of the torus and is suboptimal. However it produces good trajectories and among all possible smoothing spline it does very well in terms of the cost function.

Penalized splines have gained much popularity as a flexible tool for smoothing and semi-parametric models. Two approaches have been advocated: 1) use a B-spline basis, equally-spaced knots and difference penalties (Eilers and Marx, 1996) and 2) use truncated power functions, knots based on quantiles of the independent variable and a ridge penalty (Ruppert, Wand and Carroll, 2003). We compare th...

This paper describes a method for estimating insurance claims or risk premiums allowing for spatial dependence as well as explanatory factors. The concepts are related to those used for graduation of mortality tables using cubic splines but extended to spatial dependence as found in many insurance products. Firstly techniques for measuring spatial dependence are reviewed. Then models with bivar...

The Stanford Heart Transplant data were collected to model survival in patients using penalized smoothing splines for covariates whose values change over the course of the study. The basic idea of the present study is to use a logistic regression model and a generalized additive model with B-splines to estimate the survival function. We model survival time as a function of patient covariates an...

Vector smoothing splines on the sphere are defined% Theoretical properties are briefly alluded to. An approach to choosing the appropriate Hilbert space norms to use in a specific meteorological application is described and justified via a duality theorem. Numerical procedures for computing the splines as well as the cross validation estimate of two smoothing parameters are given. A Monte Carlo...