Binder, Harald

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

This thesis presents new models and estimation techniques based onthe generalized linear model framework.In Chapter 1 the GAMBoost procedure for estimation of generalizedadditive models is developed. Based on boosting and gradient descentin function space it generalizes the notion of repeated fitting ofresiduals to exponential family responses. By using a flexible numberof updates for each covariate the selection of smoothing parametersis reduced to the selection of the number of boosting steps. Thelatter is chosen based on approximate effective degrees of freedom.The resulting procedure shows good performance for a wide variety ofexamples with binary and Poisson response data. A considerableadvantage compared to other procedures is found for a large number ofcovariates and a low level of information. An application to realdata is presented.In Chapter 2 a flexible model for discrete time survival data isdeveloped that allows for non-linear covariate effects that vary overtime. For estimation an iterative two-step procedure based on Fisherscoring is given. A simulation study with various levels ofcomplexity underlying the data compares the performance of adequatemodels to the performance of models that are too restrictive, tooflexible or that provide the wrong kind of flexibility. It is shownthat effective degrees of freedom work well as a basis for selectionof smoothing parameters as well as for model selection. An examplewith real data is given.In Chapter 3 a technique for classification with binary response datais developed based on logistic regression. It uses local models withlocal selection of predictors for reduction of complexity andpenalized estimation for numerical stability.Standard simulated data examples are used to evaluate components ofthe algorithm such as the kernel for local weight calculation, and tocompare the performance to other procedures. It is found that theprocedure is competitive for a wide range of examples and thatselection of predictors is crucial for local quadratic models whilebeing regulated rather well for local linear models.Good performance can also be seen for real data examples.