EconStor Collection:
http://hdl.handle.net/10419/158
2017-05-22T19:36:36ZWavelets 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.2007-01-01T00:00:00ZThe effect of single-axis sorting on the estimation of a linear regression
http://hdl.handle.net/10419/31097
Title: The effect of single-axis sorting on the estimation of a linear regression
Authors: Schmid, Matthias
Abstract: Microaggregation is one of the most important statistical disclosure control techniques for continuous data. The basic principle of microaggregation is to group the observations in a data set and to replace them by their corresponding group means. In this paper, we consider single-axis sorting, a frequently applied microaggregation technique where the formation of groups depends on the magnitude of a sorting variable related to the variables in the data set. The paper deals with the impact of this technique on a linear model in continuous variables. We show that parameter estimates are asymptotically biased if the sorting variable depends on the response variable of the linear model. Using this result, we develop a consistent estimator that removes the aggregation bias. Moreover, we derive the asymptotic covariance matrix of the corrected least squares estimator.2006-01-01T00:00:00ZRisk performance of Stein-rule estimators over the least squares estimators of regression coefficients under quadratic loss structures
http://hdl.handle.net/10419/31089
Title: Risk performance of Stein-rule estimators over the least squares estimators of regression coefficients under quadratic loss structures
Authors: Shalabh; Toutenburg, Helge; Heumann, Christian
Abstract: This paper presents a general loss function under quadratic loss structure and discusses the comparison of risk functions associated with the unbiased least squares and biased Stein-rule estimators of the coefficients in a linear regression model.2006-01-01T00:00:00Z