Penalized splines have become an increasingly popular tool for nonparametric smoothing because of their use of low-rank spline bases, which makes computations tractable while maintaining accuracy as good as smoothing splines. This article extends penalized spline methodology by both modeling the variance function nonparametrically and using a spatially adaptive smoothing parameter. This combina...

Shape restricted smoothing splines receive growing attention, motivated by a wide range of important applications in science and engineering. In this paper, we consider smoothing splines subject to general linear dynamics and control constraints, and formulate them as finite-horizon constrained linear optimal control problems with unknown initial state and control. By exploring techniques from ...

It is widely known that, in a certain sense, a smoothing spline estimate of the regression function is asymptotically equivalent to a kernel regression estimate. However, little information has been available about the equivalence between nonparametric regression tests, based on the smoothing spline and local polynomial regression methods. To assess their relative behaviors and to facilitate il...

This paper explores the productivity impact of information technology (IT) in the healthcare industry using a regression spline (RS)-based approach. Application of the RS-based approach offered additional valuable insights that contribute to our understanding of the complex relationship between investments in IT and organizational productivity. For example, the results of this study suggest tha...

This paper examines the application of a bootstrap test error estimation of radial basis functions, specifically thin-plate spline fitting, in surface smoothing. The presence of noisy data is a common issue of the point set model that is generated from 3D scanning devices, and hence, point set denoising is one of the main concerns in point set modelling. Bootstrap test error estimation, which i...

This dissertation consists of three parts: the first two parts are related to smoothing spline ANOVA models; the third part concerns the Lasso and its related procedures in model selection. In Part I, by adopting the Cox proportional hazard model to quantify the hazard function, we propose a novel nonparametric model selection technique to analyze time to event data, within the framework of smo...

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...

In this work we present a new approach to two dimensional robust spline smoothing. The proposed method is based on M-estimator algorithms but unlike in other M-estimator based image processing algorithms it takes into consideration spatial relations between picture elements. The contribution of the sample to the model depends not only on the current residual of that sample, but also on the neig...

This paper looks into the intonational use of pitch in Cantonese English. It aims at providing phonetic evidence for the intonation of statements and questions in interaction with tones identified at lexical level. A smoothing spline analysis of variance was fitted to the audio-recording data from six speakers of Cantonese English with R in order to generate smoothing splines at 95% confidence ...

In some applications, especially spectrometric ones, curve classifiers achieve better performances if they work on the m-order derivatives of their inputs. This paper proposes a smoothing spline based approach that give a strong theoretical background to this common practice.