Flexible Semi- and Non-Parametric Modelling and Prognosis for Discrete Outcomes

This thesis presents new models and estimation techniques based on
the generalized linear model framework.
In Chapter 1 the GAMBoost procedure for estimation of generalized
additive models is developed. Based on boosting and gradient descent
in function space it generalizes the notion of repeated fitting of
residuals to exponential family responses. By using a flexible number
of updates for each covariate the selection of smoothing parameters
is reduced to the selection of the number of boosting steps. The
latter is chosen based on approximate effective degrees of freedom.
The resulting procedure shows good performance for a wide variety of
examples with binary and Poisson response data. A considerable
advantage compared to other procedures is found for a large number of
covariates and a low level of information. An application to real
data is presented.

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.