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    <title>EconStor Community: Sonderforschungsbereich 386: Statistische Analyse diskreter Strukturen, Universität München (LMU)</title>
    <link>http://hdl.handle.net/10419/157</link>
    <description>Collaborative Research Center (SFB) 386: Statistical Analysis of discrete structures - Applications in Biometrics and Econometrics, LMU Munich</description>
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  <item rdf:about="http://hdl.handle.net/10419/31160">
    <title>On association in regression: the coefficient of determination revisited</title>
    <link>http://hdl.handle.net/10419/31160</link>
    <description>Title: On association in regression: the coefficient of determination revisited
&lt;br/&gt;
&lt;br/&gt;Authors: van der Linde, A.; Tutz, Gerhard</description>
  </item>
  <item rdf:about="http://hdl.handle.net/10419/31159">
    <title>Variable selection and discrimination in gene expression data by genetic algorithms</title>
    <link>http://hdl.handle.net/10419/31159</link>
    <description>Title: Variable selection and discrimination in gene expression data by genetic algorithms
&lt;br/&gt;
&lt;br/&gt;Authors: Krause, Rüdiger; Tutz, Gerhard
&lt;br/&gt;
&lt;br/&gt;Abstract: Gene expression datasets usually have thousends of explanatory variables which are observed on only few samples. Generally most variables of a dataset have no effect and one is interested in eliminating these irrelevant variables. In order to obtain a subset of relevant variables an appropriate selection procedure is necessary. In this paper we propose the selection of variables by use of genetic algorithms with the logistic regression as underlying modelling procedure. The selection procedure aims at minimizing information criteria like AIC or BIC. It is demonstrated that selection of variables by genetic algorithms yields models which compete well with the best available classification procedures in terms of test misclassification error.</description>
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  <item rdf:about="http://hdl.handle.net/10419/31158">
    <title>Knot selection by boosting techniques</title>
    <link>http://hdl.handle.net/10419/31158</link>
    <description>Title: Knot selection by boosting techniques
&lt;br/&gt;
&lt;br/&gt;Authors: Leitenstorfer, Florian; Tutz, Gerhard
&lt;br/&gt;
&lt;br/&gt;Abstract: A novel concept for estimating smooth functions by selection techniques based on boosting is developed. It is suggested to put radial basis functions with different spreads at each knot and to do selection and estimation simultaneously by a componentwise boosting algorithm. The methodology of various other smoothing and knot selection procedures (e.g. stepwise selection) is summarized. They are com- pared to the proposed approach by extensive simulations for various unidimensional settings, including varying spatial variation and heteroskedasticity, as well as on a real world data example. Finally, an extension of the proposed method to surface fitting is evaluated numerically on both, simulation and real data. The proposed knot selection technique is shown to be a strong competitor to existing methods for knot selection. - Nonparametric regression ; Knot selection ; Radial basis functions ; Boosting ; Surface fitting</description>
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  <item rdf:about="http://hdl.handle.net/10419/31157">
    <title>Bayesian learning for a class of priors with prescribed marginals</title>
    <link>http://hdl.handle.net/10419/31157</link>
    <description>Title: Bayesian learning for a class of priors with prescribed marginals
&lt;br/&gt;
&lt;br/&gt;Authors: Held, Hermann; Kriegler, Elmar; Augustin, Thomas
&lt;br/&gt;
&lt;br/&gt;Abstract: We present Bayesian updating of an imprecise probability measure, represented by a class of precise multidimensional probability measures. Choice and analysis of our class are motivated by expert interviews that we conducted with modelers in the context of climatic change. From the interviews we deduce that generically, experts hold a much more informed opinion on the marginals of uncertain parameters rather than on their correlations. Accordingly, we specify the class by prescribing precise measures for the marginals while letting the correlation structure subject to complete ignorance. For sake of transparency, our discussion focuses on the tutorial example of a linear two-dimensional Gaussian model. We operationalize Bayesian learning for that class by various updating rules, starting with (a modified version of) the generalized Bayes' rule and the maximum likelihood update rule (after Gilboa and Schmeidler). Over a large range of potential observations, the generalized Bayes' rule would provide non-informative results. We restrict this counter-intuitive and unnecessary growth of uncertainty by two means, the discussion of which refers to any kind of imprecise model, not only to our class. First, we find our class of priors too inclusive and, hence, require certain additional properties of prior measures in terms of smoothness of probability density functions. Second, we argue that both updating rules are dissatisfying, the generalized Bayes' rule being too conservative, i.e., too inclusive, the maximum likelihood rule being too exclusive. Instead, we introduce two new ways of Bayesian updating of imprecise probabilities: a weighted maximum likelihood method and a semi-classical method. The former bases Bayesian updating on the whole set of priors, however, with weighted influence of its members. By referring to the whole set, the weighted maximum likelihood method allows for more robust inferences than the standard maximum likelihood method and, hence, is better to justify than the latter. Furthermore, the semi-classical method is more objective than the weighted maximum likelihood method as it does not require the subjective definition of a weighting function. Both new methods reveal much more informative results than the generalized Bayes' rule, what we demonstrate for the example of a stylized insurance model.</description>
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