Approximating data with weighted smoothing splines

n.a. --Approximation,Residuals,Smoothing Splines,Thin Plate Splines

Resistant Nonparametric Smoothing with S-PLUS

In this paper we introduce and illustrate the use of an S-PLUS set of functions to fit M-type smoothing splines with the smoothing parameter chosen by a robust criterion (either a robust version of cross-validation or a robust version of Mallows's Cp ). The main reference is: Cantoni, E. and Ronchetti, E. (2001). Resistant selection of the smoothing parameter for smoothing splines. Statistics and Computing, 11, 141-146.

Smoothing splines with varying smoothing parameter

This paper considers the development of spatially adaptive smoothing splines for the estimation of a regression function with non-homogeneous smoothness across the domain. Two challenging issues that arise in this context are the evaluation of the equivalent kernel and the determination of a local penalty. The roughness penalty is a function of the design points in order to accommodate local behavior of the regression function. It is shown that the spatially adaptive smoothing spline estimator is approximately a kernel estimator. The resulting equivalent kernel is spatially dependent. The equivalent kernels for traditional smoothing splines are a special case of this general solution. With the aid of the Green's function for a two-point boundary value problem, the explicit forms of the asymptotic mean and variance are obtained for any interior point. Thus, the optimal roughness penalty function is obtained by approximately minimizing the asymptotic integrated mean square error. Simulation results and an application illustrate the performance of the proposed estimator

Vector splines on the sphere with application to the estimation of vorticity and divergence from discrete, noisy data

Vector smoothing splines on the sphere are defined. Theoretical properties are briefly alluded to. The appropriate Hilbert space norms used in a specific meteorological application are 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 study is described which suggests the accuracy with which upper air vorticity and divergence can be estimated using measured wind vectors from the North American radiosonde network

Semiparametric models and P-splines

P-splines were introduced by Eilers and Marx (1996). We consider semiparametric models where the smooth part of the model can be described by P-splines. A mixed model representation is also considered. We set a simple strategy for the choice of P-spline parameters, ndx, bdeg and pord, and discuss the use of various criteria for smoothing parameter selection. We illustrate our remarks with the analysis of a randomised block design

Semiparametric estimation for a class of time-inhomogenous diffusion processes

Copyright @ 2009 Institute of Statistical Science, Academia SinicaWe develop two likelihood-based approaches to semiparametrically estimate a class of time-inhomogeneous diffusion processes: log penalized splines (P-splines) and the local log-linear method. Positive volatility is naturally embedded and this positivity is not guaranteed in most existing diffusion models. We investigate different smoothing parameter selections. Separate bandwidths are used for drift and volatility estimation. In the log P-splines approach, different smoothness for different time varying coefficients is feasible by assigning different penalty parameters. We also provide theorems for both approaches and report statistical inference results. Finally, we present a case study using the weekly three-month Treasury bill data from 1954 to 2004. We find that the log P-splines approach seems to capture the volatility dip in mid-1960s the best. We also present an application to calculate a financial market risk measure called Value at Risk (VaR) using statistical estimates from log P-splines