| dc.contributor.advisor | Kneib, Thomas Prof. Dr. | |
| dc.contributor.author | Säfken, Benjamin | |
| dc.date.accessioned | 2015-04-10T09:46:53Z | |
| dc.date.available | 2015-04-10T09:46:53Z | |
| dc.date.issued | 2015-04-10 | |
| dc.identifier.uri | http://hdl.handle.net/11858/00-1735-0000-0022-5FA9-B | |
| dc.identifier.uri | http://dx.doi.org/10.53846/goediss-5020 | |
| dc.language.iso | eng | de |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/ | |
| dc.subject.ddc | 510 | de |
| dc.title | Model choice and variable selection in mixed & semiparametric models | de |
| dc.type | doctoralThesis | de |
| dc.contributor.referee | Kneib, Thomas Prof. Dr. | |
| dc.date.examination | 2015-03-27 | |
| dc.description.abstracteng | Semiparametric and mixed models allow different kinds of data structures and
data types to be considered in regression models. Spatial and temporal
structures of discrete or spatial data can be treated as flexibly as, for
instance, functional data. This growing flexibility increasingly requires a
statistician to make choices between competing models.
In model selection the degrees of freedom play an important role as a measure of
model complexity. In this thesis three approaches for the estimation of the
degrees of freedom in mixed and semiparametric models are developed, each for
different distributions of the (conditional) responses. The interpretation of
semiparametric models as mixed models justifies using the same model selection
techniques for both model classes.
By using Steinian methods, the degrees of freedom can be determined for a
group of distributions belonging to the exponential family. The developed
methods for determining the degrees of freedom are illustrated by an example of
tree growth data.
For a larger class of distributions the degrees of freedom can be determined by
cross-validation and bootstrap methods. Additionally, an approximate Steinian
method can be adapted for further distributions.
Based on the implicit function theorem the degrees of freedom of a variance or
smoothing parameter can de derived analytically if the response is normally
distributed. Failure to take these degrees of freedom into account can lead to
biased model selection. In addition to the methodological derivation, the
geometrical properties of the degrees of freedom of the variance and smoothing
parameters are analysed. Furthermore, numerical problems in the computation of
the degrees of freedom are considered. | de |
| dc.contributor.coReferee | Krivobokova, Tatyana Prof. Dr. | |
| dc.subject.eng | semiparametric regression | de |
| dc.subject.eng | mixed model | de |
| dc.subject.eng | model selection | de |
| dc.identifier.urn | urn:nbn:de:gbv:7-11858/00-1735-0000-0022-5FA9-B-9 | |
| dc.affiliation.institute | Fakultät für Mathematik und Informatik | de |
| dc.subject.gokfull | Mathematics (PPN61756535X) | de |
| dc.identifier.ppn | 821928384 | |