Filters

2013 - 20143

More filters

20193
Reset filters

Settings

Author: Stange, Jens ×

Search Results

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Computing and approximating multivariate chi-square probabilities
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Stange, Jens; Loginova, Nina; Dickhaus, Thorsten
    We consider computational methods for evaluating and approximating multivariate chi-square probabilities in cases where the pertaining correlation matrix or blocks thereof have a low-factorial representation. To this end, techniques from matrix factorization and probability theory are applied. We outline a variety of statistical applications of multivariate chi-square distributions and provide a system of MATLAB programs implementing the proposed algorithms. Computer simulations demonstrate the accuracy and the computational efficiency of our methods in comparison with Monte Carlo approximations, and a real data example from statistical genetics illustrates their usage in practice.
  • Thumbnail Image
    Item
    On an extended interpretation of linkage disequilibrium in genetic case-control association studies
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Dickhaus, Thorsten; Stange, Jens; Demirhan, Haydar
    We are concerned with statistical inference for 2 x 2 x K contingency tables in the context of genetic case-control association studies. Multivariate methods based on asymptotic Gaussianity of vectors of test statistics require information about the asymptotic correlation structure among these test statistics under the global null hypothesis. We show that for a wide variety of test statistics this asymptotic correlation structure is given by the linkage disequilibrium matrix of the K loci under investigation. Three popular choices of test statistics are discussed for illustration.
  • Thumbnail Image
    Item
    Uncertainty quantification for the family-wise error rate in multivariate copula models
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Stange, Jens; Bodnar, Taras; Dickhaus, Thorsten
    We derive confidence regions for the realized family-wise error rate (FWER) of certain multiple tests which are empirically calibrated at a given (global) level of significance. To this end, we regard the FWER as a derived parameter of a multivariate parametric copula model. It turns out that the resulting onfidence regions are typically very much concentrated around the target FWER level, while generic multiple tests with fixed thresholds are in general not FWER-exhausting. Since FWER level exhaustion and optimization of power are equivalent for the classes of multiple test problems studied in this paper, the aforementioned findings militate strongly in favour of estimating the dependency structure (i. e., copula) and incorporating it in a multivariate multiple test procedure. We illustrate our theoretical results by considering two particular classes of multiple test problems of practical relevance in detail, namely, multiple tests for components of a mean vector and multiple support tests.