In Chapter 2 a flexible model for discrete time survival data is developed that allows for non-linear covariate effects that vary over time. For estimation an iterative two-step procedure based on Fisher scoring is given. A simulation study with various levels of complexity underlying the data compares the performance of adequate models to the performance of models that are too restrictive, too flexible or that provide the wrong kind of flexibility. It is shown that effective degrees of freedom work well as a basis for selection of smoothing parameters as well as for model selection. An example with real data is given.
In Chapter 3 a technique for classification with binary response data
is developed based on logistic regression. It uses local models with
local selection of predictors for reduction of complexity and
penalized estimation for numerical stability.
Standard simulated data examples are used to evaluate components of the algorithm such as the kernel for local weight calculation, and to compare the performance to other procedures. It is found that the procedure is competitive for a wide range of examples and that selection of predictors is crucial for local quadratic models while being regulated rather well for local linear models. Good performance can also be seen for real data examples.