Longitudinal trends of observations can be estimated using the generalized multivariate analysis of variance (GMANOVA) model proposed by [10]. In the present paper, we consider estimating the trends nonparametrically using known basis functions. Then, as in nonparametric regression, an overfitting problem occurs. [13] showed that the GMANOVA model is equivalent to the varying coefficient model ...

Although the literature on varying coefficient models (VCMs) is vast, we believe that there remains room to make these models more widely accessible and provide a unified and practical implementation for a variety of complex data settings. The adaptive nature and strength of P-spline VCMs allow a full range of models: from simple to additive structures, from standard to generalized linear model...

Abstract: Two existing approaches to functional principal components analysis (FPCA) are due to Rice and Silverman (1991) and Silverman (1996), both based on maximizing variance but introducing penalization in different ways. In this article we propose an alternative approach to FPCA using penalized rank one approximation to the data matrix. Our contributions are four-fold: (1) by considering i...

B-SPLINE MODELING AND ESTIMATOR PERFORMANCE Stephen R. Titus, Alfred O. Hero III, Je rey A. Fessler Department of EECS University of Michigan Ann Arbor, MI 48109 [email protected] ABSTRACT We give estimation error bounds and specify optimal estimators for continuous, closed boundary curves in an NMR image. The boundary is parameterized using periodic B-Splines. A Cramer-Rao lower bound on ...

Modelling walking distance enables the observation of non-linearities in hedonic property pricing accessibility to greenspace. We test a penalized spline spatial error model (PS-SEM), which has two distinctive features. First, PS-SEM controls for presence spatially autocorrelated term. Second, allows continuous non-linear decay price premium as function greenspaces. As result, compared with tra...

Smoothing splines via the penalized least squares method provide versatile and effective nonparametric models for regression with Gaussian responses. The computation of smoothing splines is generally of the order O.n3/, n being the sample size, which severely limits its practical applicability. We study more scalable computation of smoothing spline regression via certain low dimensional approxi...

It is argued that the Calibrated Bayesian (CB) approach to statistical inference capitalizes on the strength of Bayesian and frequentist approaches to statistical inference. In the CB approach, inferences under a particular model are Bayesian, but frequentist methods are useful for model development and model checking. In this article the CB approach is outlined. Bayesian methods for missing da...

Penalized splines have become a popular tool to model the trend component in economic time series. The outcome of the spline predominantly depends on the choice of a penalization parameter that controls the smoothness of the trend. This paper derives the penalization of splines by frequency domain aspects and points out their link to rational square wave filters. As a novel contribution this pa...

This article is motivated by an application where subjects were dosed three times with the same drug and the drug concentration profiles appeared to be the lowest after the third dose. One possible explanation is that the pharmacokinetic (PK) parameters vary over time. Therefore, we consider population PK models with time-varying PK parameters. These time-varying PK parameters are modeled by na...

Current approaches to quantitative analysis of DCE-MRI with non-linear models involve the convolution of an arterial input function (AIF) with the contrast agent concentration at a voxel or regional level. Full quantification provides meaningful biological parameters but is complicated by the issues related to convergence, (de-)convolution of the AIF, and goodness of fit. To overcome these prob...