Fakultät für Statistik
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Item Flexible specification testing in quantile regression models(2023-08-01) Kutzker, Tim; Klein, Nadja; Wied, DominikWe propose three novel consistent specification tests for quantile regression models which generalize former tests in three ways. First, we allow the covariate effects to be quantile-dependent and nonlinear. Second, we allow parameterizing the conditional quantile functions by appropriate basis functions, rather than parametrically. We are thereby able to test for general functional forms, while retaining linear effects as special cases. In both cases, the induced class of conditional distribution functions is tested with a Cramér–von Mises type test statistic for which we derive the theoretical limit distribution and propose a bootstrap method. Third, a modified test statistic is derived to increase the power of the tests. We highlight the merits of our tests in a detailed MC study and two real data examples. Our first application to conditional income distributions in Germany indicates that there are not only still significant differences between East and West but also across the quantiles of the conditional income distributions, when conditioning on age and year. The second application to data from the Australian national electricity market reveals the importance of using interaction effects for modeling the highly skewed and heavy-tailed distributions of energy prices conditional on day, time of day and demand.Item Designs for the simultaneous inference of concentration–response curves(2023-10-19) Schürmeyer, Leonie; Schorning, Kirsten; Rahnenführer, JörgBackground: An important problem in toxicology in the context of gene expression data is the simultaneous inference of a large number of concentration–response relationships. The quality of the inference substantially depends on the choice of design of the experiments, in particular, on the set of different concentrations, at which observations are taken for the different genes under consideration. As this set has to be the same for all genes, the efficient planning of such experiments is very challenging. We address this problem by determining efficient designs for the simultaneous inference of a large number of concentration–response models. For that purpose, we both construct a D-optimality criterion for simultaneous inference and a K-means procedure which clusters the support points of the locally D-optimal designs of the individual models. Results: We show that a planning of experiments that addresses the simultaneous inference of a large number of concentration–response relationships yields a substantially more accurate statistical analysis. In particular, we compare the performance of the constructed designs to the ones of other commonly used designs in terms of D-efficiencies and in terms of the quality of the resulting model fits using a real data example dealing with valproic acid. For the quality comparison we perform an extensive simulation study. Conclusions: The design maximizing the D-optimality criterion for simultaneous inference improves the inference of the different concentration–response relationships substantially. The design based on the K-means procedure also performs well, whereas a log-equidistant design, which was also included in the analysis, performs poorly in terms of the quality of the simultaneous inference. Based on our findings, the D-optimal design for simultaneous inference should be used for upcoming analyses dealing with high-dimensional gene expression data.Item Optimal designs for comparing regression curves: dependence within and between groups(2021-11-26) Schorning, Kirsten; Dette, HolgerWe consider the problem of designing experiments for the comparison of two regression curves describing the relation between a predictor and a response in two groups, where the data between and within the group may be dependent. In order to derive efficient designs we use results from stochastic analysis to identify the best linear unbiased estimator (BLUE) in a corresponding continuous model. It is demonstrated that in general simultaneous estimation using the data from both groups yields more precise results than estimation of the parameters separately in the two groups. Using the BLUE from simultaneous estimation, we then construct an efficient linear estimator for finite sample size by minimizing the mean squared error between the optimal solution in the continuous model and its discrete approximation with respect to the weights (of the linear estimator). Finally, the optimal design points are determined by minimizing the maximal width of a simultaneous confidence band for the difference of the two regression functions. The advantages of the new approach are illustrated by means of a simulation study, where it is shown that the use of the optimal designs yields substantially narrower confidence bands than the application of uniform designs.Item Exchange rate pass-through to import prices in Europe(2020-04-10) Arsova, AntoniaThis paper takes a panel cointegration approach to the estimation of short- and long-run exchange rate pass-through (ERPT) to import prices in the European countries. Although economic theory suggests a long-run relationship between import prices and exchange rate, in recent empirical studies its existence has either been overlooked or it has proven difficult to establish. Resorting to novel tests for panel cointegration, we find support for the equilibrium relationship hypothesis. Exchange rate pass-through elasticities, estimated by two different techniques for cointegrated panel regressions, give insight into the most recent development of the ERPT.Item Generalised joint regression for count data(2020-06-25) Wurp, Hendrik van der; Groll, Andreas; Kneib, Thomas; Marra, Giampiero; Radice, RosalbaWe propose a versatile joint regression framework for count responses. The method is implemented in the R add-on package GJRM and allows for modelling linear and non-linear dependence through the use of several copulae. Moreover, the parameters of the marginal distributions of the count responses and of the copula can be specified as flexible functions of covariates. Motivated by competitive settings, we also discuss an extension which forces the regression coefficients of the marginal (linear) predictors to be equal via a suitable penalisation. Model fitting is based on a trust region algorithm which estimates simultaneously all the parameters of the joint models. We investigate the proposal’s empirical performance in two simulation studies, the first one designed for arbitrary count data, the other one reflecting competitive settings. Finally, the method is applied to football data, showing its benefits compared to the standard approach with regard to predictive performance.Item Dieter Rasch, Rob Verdooren and Jürgen Pilz: Applied statistics: theory and problem solutions with R(2020-02-06) Krämer, Walter