ABSTRACT

Automatic smoothing parameter selection methods for nonparametric regression like cross-validation and generalized cross-validation are known to be severely affected by dependence in the regression errors. We proposed, in this work, to modify some of the ideas used in the cross-validation criterion in kernel regression with dependent errors and apply them to smoothing splines with model based penalty. Model based penalty smoothing permits us to keep the flexibility of the nonparametric methods while it also allows us to specify a favoured parametric model which can help improve on the estimate of the regression function.

We consider the ``modified cross-validation'' (also known as Leave-2l+1 out) and the ``blockwise cross-validation'' smoothing parameter selection techniques which were initially proposed by Wehrly and Hart (1988) and Hardle and Vieu (1992) respectively. These two smoothing parameter selection techniques take correlation into account and alleviate its effect on the regression function estimation.

We use a simulation study to evaluate the performance of our two smoothing parameter selection techniques. We compare the results with a few commonly used parametric techniques. Our techniques are also applied to an air pollution data set where we estimate the underlying trend of daily and monthly ground ozone levels in southern Ontario.

Chapter 0: Abstract, table of contents, list of tables and figures.