EconStor Collection:
http://hdl.handle.net/10419/158
2016-06-25T05:22:09ZWavelets for diffusion tensor imaging
http://hdl.handle.net/10419/31074
Title: Wavelets for diffusion tensor imaging
Authors: Heim, Susanne
Abstract: In this paper, wavelet basis functions are investigated for their suitability for processing and analysing diffusion tensor imaging (DTI) data. First, wavelet theory is introduced and explained by means of 1d and 2d examples (Section 1.1 - 1.3). General thresholding techniques, which serve as regularization concepts for wavelet based models, are presented in Section 1.4. Regularization of DTI data can be performed at two stages, either immediately after acquisition (Wirestam et al., 2006) or after tensor estimation. The latter stage of denoising is outlined in Section 6 together with the incorporation of the positive definiteness constraint using log-Cholesky parametrization. In Section 3, the procedure is examined in a simulation study and compared to standard processing and the space-varying coefficient model (SVCM) based on B-spines (Heim et al., 2007). In addition, a real data example is presented and discussed. Finally, an approach is proposed how a space-varying coefficient model could fairly be adapted to wavelet basis functions. The theoretical parts are based on books of Gencay et al. (2002, Chap. 1, 4-6), HÃ¤rdle et al. (1998), Ogden (1997) and Jansen (2001) if not stated otherwise. For an introduction to diffusion tensor imaging refer to Heim et al. (2007, Chap. 2).2007-01-01T00:00:00ZA diffusion approximation for an epidemic model
http://hdl.handle.net/10419/31042
Title: A diffusion approximation for an epidemic model
Authors: Dargatz, Christiane
Abstract: Influenza is one of the most common and severe diseases worldwide. Devastating epidemics actuated by a new subtype of the influenza A virus occur again and again with the most important example given by the Spanish Flu in 1918/19 with more than 27 million deaths. For the development of pandemic plans it is essential to understand the character of the dissemination of the disease. We employ an extended SIR model for a probabilistic analysis of the spatio-temporal spread of influenza in Germany. The inhomogeneous mixing of the population is taken into account by the introduction of a network of subregions, connected according to Germany's commuter and domestic air traffic. The infection dynamics is described by a multivariate diffusion process, the discussion of which is a major part of this report. We furthermore present likelihood-based estimates of the model parameters.2007-01-01T00:00:00ZMaximally selected chi-square statistics and umbrella orderings
http://hdl.handle.net/10419/30998
Title: Maximally selected chi-square statistics and umbrella orderings
Authors: Boulesteix, Anne-Laure; Strobl, Carolin
Abstract: Binary outcomes that depend on an ordinal predictor in a nonmonotonic way are common in medical data analysis. Such patterns can be addressed in terms of cutpoints: for example, one looks for two cutpoints that define an interval in the range of the ordinal predictor for which the probability of a positive outcome is particularly high (or low). A chi-square test may then be performed to compare the proportions of positive outcomes in and outside this interval. However, if the two cutpoints are chosen to maximize the chi-square statistic, referring the obtained chi-square statistic to the standard chi-square distribution is an inappropriate approach. It is then necessary to correct the p-value for multiple comparisons by considering the distribution of the maximally selected chi-square statistic instead of the nominal chi-square distribution. Here, we derive the exact distribution of the chi-square statistic obtained by the optimal two cutpoints. We suggest a combinatorial computation method and illustrate our approach by a simulation study and an application to varicella data.2006-01-01T00:00:00ZZero-inflated generalized Poisson models with regression effects on the mean, dispersion and zero-inflation level applied to patent outsourcing rates
http://hdl.handle.net/10419/30994
Title: Zero-inflated generalized Poisson models with regression effects on the mean, dispersion and zero-inflation level applied to patent outsourcing rates
Authors: Czado, Claudia; Erhardt, Vinzenz; Min, Aleksey
Abstract: This paper focuses on an extension of zero-inflated generalized Poisson (ZIGP) regression models for count data. We discuss generalized Poisson (GP) models where dispersion is modelled by an additional model parameter. Moreover, zero-inflated models in which overdispersion is assumed to be caused by an excessive number of zeros are discussed. In addition to ZIGP regression introduced by Famoye and Singh (2003), we now allow for regression on the overdispersion and zero-inflation parameters. Consequently, we propose tools for an exploratory data analysis on the dispersion and zero-inflation level. An application dealing with outsourcing of patent filing processes will be used to compare these nonnested models. The model parameters are fitted by maximum likelihood. Asymptotic normality of the ML estimates in this non-exponential setting is proven. Standard errors are estimated using the asymptotic normality of the estimates. Appropriate exploratory data analysis tools are developed. Also, a model comparison using AIC statistics and Vuong tests (see Vuong (1989)) is carried out. For the given data, our extended ZIGP regression model will prove to be superior over GP and ZIP models and even ZIGP models with constant overall dispersion and zero-inflation parameters demonstrating the usefulness of our proposed extensions.2006-01-01T00:00:00Z