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...

We propose a novel framework that combines penalization techniques with Partial Least Squares (PLS). We focus on two important applications. (1) We combine PLS with a roughness penalty to estimate high-dimensional regression problems with functional predictors and scalar response. (2) Starting with an additive model, we expand each variable in terms of a generous number of B-Spline basis functi...

We propose a general approach to regression on digitized multidimensional signals that can pose severe challenges to standard statistical methods. The main contribution of this work is to build a two-dimensional coefficient surface that allows for interaction across the indexing plane of the regressor array. We aim to use the estimated coefficient surface for reliable (scalar) prediction. We as...

In this paper we study penalized regression splines (P-splines), which are low–order basis function splines with a penalty to avoid undersmoothing. Such P–splines are typically not spatially adaptive, and hence can have trouble when functions are varying rapidly. While frequentist methods are available to address this issue, no Bayesian techniques have been developed. Our approach is to model t...

OBJECTIVE Improving and validating sleep scoring algorithms for actigraphs enhances their usefulness in clinical and research applications. The MTI® device (ActiGraph, Pensacola, FL) had not been previously validated for sleep. The aims were to (1) compare the accuracy of sleep metrics obtained via wrist- and hip-mounted MTI® actigraphs with polysomnographic (PSG) recordings in a sample that in...

The Isogeometric Analysis (IA) method is applied for structural topology optimization instead of the finite element method. For this purpose, the material density is considered as a continuous function throughout the design domain and approximated by the Non-Uniform Rational B-Spline (NURBS) basis functions. The coordinates of control points which are also used for constructing the density func...

This paper focuses on self-similar gravitational collapse solutions of the Einstein--axion-dilaton configuration for two conjugacy classes SL(2, R) transformations. These are invariant under spacetime dilation, combined with internal For first time in literature, we apply nonlinear statistical spline regression methods to estimate critical spherical black hole four dimension. include truncated ...