Some Problems in Model Specification and Inference for Generalized Additive Models

  • Giampiero Marra

Student thesis: Doctoral ThesisPhD

Abstract

Regression models describingthe dependence between a univariate response and a set of covariates play a fundamental role in statistics. In the last two decades, a tremendous effort has been made in developing flexible regression techniques such as generalized additive models(GAMs) with the aim of modelling the expected value of a response variable as a sum of smooth unspecified functions of predictors. Many nonparametric regression methodologies exist includinglocal-weighted regressionand smoothing splines. Here the focus is on penalized regression spline methods which can be viewed as a generalization of smoothing splines with a more flexible choice of bases and penalties. This thesis addresses three issues. First, the problem of model misspecification is treated by extending the instrumental variable approach to the GAM context. Second, we study the theoretical and empirical properties of the confidence intervals for the smooth component functions of a GAM. Third, we consider the problem of variable selection within this flexible class of models. All results are supported by theoretical arguments and extensive simulation experiments which shed light on the practical performance of the methods discussed in this thesis.
Date of Award1 Dec 2010
LanguageEnglish
Awarding Institution
  • University of Bath
SupervisorSimon Wood (Supervisor)

Keywords

  • instrumental variable
  • generalized additive model
  • confidence intervals
  • variable selection

Cite this

Some Problems in Model Specification and Inference for Generalized Additive Models
Marra, G. (Author). 1 Dec 2010

Student thesis: Doctoral ThesisPhD