John H.J. Einmahl (Tilburg University)
"Empirical likelihood based testing for multivariate regular variation"
Multivariate regular variation is an important property of a multivariate probability distribution that can be very useful in extreme value statistics. Therefore it is desirable to check this property based on a multivariate random sample. We construct a hypothesis test for multivariate regular variation based on localized empirical likelihood and establish its limiting null distribution. We also investigate the finite sample performance of the test using simulated and real data. This is joint work with Andrea Krajina (Göttingen).
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Holger Rootzén (Chalmers University)
"Material structures seen through microscopes and statistics: advanced soft materials for medical and hygiene products"
This is the title of a project involving eight Chalmers researcher, five from statistics and three from applied physics, and 4 researchers from Astra-Zeneca. The goal is development of new tools for understanding of the connection between material properties and material microstructure at very high spatial resolution, for use in design of the materials of the future. One focus is on tablets with tightly controlled drug release rates. We develop new confocal laser scanning and scanning electron microscopy techniques for seeing the tablet coatings, and new statistical models and estimation techniques aimed at analysis of the images and at moving costly and time-consuming experiments from laboratories to the virtual world. Right now we work with two model classes: 3-d thresholded Gaussian fields, and point process based models. Challenges go all the way from developing new stochastic theory to optimizing very large computations. In this talk I will describe some of the advances made so far, and mention a few of the very many remaining problems we work on.
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Holger Drees (University of Hamburg)
"Conditional Extreme Value Models: Misconceptions and Pitfalls"
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Richard Davis (Columbia University)
"Applications of Distance Correlation to Time Series"
The use of empirical characteristic functions for inference problems, including estimation in some special parametric settings and testing for goodness of fit, has a long history dating back to the 70s (see for example, Feuerverger and Mureika (1977), and Csorgo (1981)). More recently, there has been renewed interest in using empirical characteristic functions in other inference settings. The distance covariance and correlation, developed by Szekely and Rizzo (2007) for measuring dependence and testing independence between two random vectors, are perhaps the best known illustrations of this. We apply these ideas to stationary univariate and multivariate time series to measure lagged auto- and cross-dependence in a time series. Assuming strong mixing, we establish the relevant asymptotic theory for the sample auto- and cross-distance correlation functions. We also apply the auto-distance correlation function (adcf) to the residuals of an autoregressive processes as a test of goodness of fit. Under the null that an autoregressive model is true, the limit distribution of the empirical adcf can differ markedly from the corresponding one based on an iid sequence. We illustrate the use of the empirical adcf for testing dependence and cross-dependence of time series in a variety of different contexts. This is joint work with Muneya Matusi, Thomas Mikosch, and Phyllis Wan.