| This thesis consists of two parts. The first part is devoted to model selection criteria based on the Kullback-Leibler distance in linear mixed effects models. Finite sample corrections of AIC are derived for these models when ML is used and when REML loglikelihood and estimation is used. The derived criteria, as well as criteria suggested in the literature are then compared through a simulation study.;The second part of this thesis is devoted to the development of model selection tools that are based on quadratic distances between probability distributions. Quadratic distances are considered as an alternative to the Kullback-Leibler distance. A criterion for model selection, called the quadratic information criterion (QICh) is derived for nonlinear regression models, and its performance is studied. A fundamental building block of quadratic distances and tools based on them is kernel selection. We show that while the normal kernel may be inappropriate in this context, its logarithm produces appropriate information criteria. Additionally, quadratic information criteria for the nonlinear mixed effects models with fixed matrix of the random effects are derived. A simulation study illustrates the behavior of the QICh criteria for different values of the tuning parameter.;Further, we apply the theory developed here on data from a study for the treatment of Hepatitis C. |
