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 Award||1 Dec 2010|
|Supervisor||Simon Wood (Supervisor)|
- instrumental variable
- generalized additive model
- confidence intervals
- variable selection