EconStor Community: Collaborative Research Center (SFB) 386: Statistical Analysis of discrete structures - Applications in Biometrics and Econometrics, LMU Munich
http://hdl.handle.net/10419/157
Collaborative Research Center (SFB) 386: Statistical Analysis of discrete structures - Applications in Biometrics and Econometrics, LMU Munich2016-10-22T16:13:47ZA 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.2007-01-01T00:00:00ZWavelets 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).2007-01-01T00:00:00ZOn the estimation of the linear relation when the error variances are known
http://hdl.handle.net/10419/31098
Title: On the estimation of the linear relation when the error variances are known
Authors: Schneeweiss, Hans; Shalabh
Abstract: The present article considers the problem of consistent estimation in measurement error models. A linear relation with not necessarily normally distributed measurement errors is considered. Three possible estimators which are constructed as different combinations of the estimators arising from direct and inverse regression are considered. The efficiency properties of these three estimators are derived and analyzed. The effect of non-normally distributed measurement errors is analyzed. A Monte-Carlo experiment is conducted to study the performance of these estimators in finite samples and the effect of a non-normal distribution of the measurement errors.2006-01-01T00:00:00ZTesting for zero-modification in count regression models
http://hdl.handle.net/10419/31110
Title: Testing for zero-modification in count regression models
Authors: Czado, Claudia; Min, Aleksey
Abstract: Count data often exhibit overdispersion and/or require an adjustment for zero outcomes with respect to a Poisson model. Zero-modified Poisson (ZMP) and zeromodified generalized Poisson (ZMGP) regression models are useful classes of models for such data. In the literature so far only score tests are used for testing the necessity of this adjustment. For this testing problem we show how poor the performance of the corresponding score test can be in comparison to the performance of Wald and likelihood ratio (LR) tests through a simulation study. In particular, the score test in the ZMP case results in a power loss of 47% compared to the Wald test in the worst case, while in the ZMGP case the worst loss is 87%. Therefore, regardless of the computational advantage of score tests, the loss in power compared to the Wald and LR tests should not be neglected and these much more powerful alternatives should be used instead. We also prove consistency and asymptotic normality of the maximum likelihood estimators in the above mentioned regression models to give a theoretical justification for Wald and likelihood ratio tests.2006-01-01T00:00:00Z