Title: Extreme value theory for the entries of a sample covariance Matrix
Abstract: We derive the point process convergence of the off-diagonal entries of a large sample covariance matrix based on iid data toward a Poisson process. We show how the dimension p = p_n tends to 1 as n tends to infinity and the tail behavior of the entries are linked. These entries constitute dependent random walks and we are interested in their joint tail behavior. Our main tools for proving these results are precise large deviation results for sums of independent random vectors. (This is joint work with Johannes Heiny (Bochum) and Jorge Yslas (Copenhagen).
Speaker: Prof. Thomas Mikosch received his doctorate from the University of St. Petersburg in 1984. Now he is a full professor at the University of Copenhagen, Publication Chair of the Bernoulli Society, the Editor-in-Chief of Extremes and Editor of the Springer Book Series Operations Research and Financial Engineering. He has received the IMS Medallion and Alexander von Humboldt Research Award in 2018. He has published around 110 articles in top journals including the Annals of Probability, the Annals of Statistics, Stochastic Processes and their Applications and the Journal of Economics. His research interests include applied stochastic processes, insurance mathematics, time series analysis, extreme value theory, and heavy-tail phenomena.
Title: Semiparametric Estimation for Max-Stable Processes with Applications to Environmental Data
Abstract: Max-stable space-time processes have been developed to study extremal dependence in space-time data. Such models are well suited for studying extremal dependence in, for example, environmental data. A semiparametric estimation procedure based on a closed form expression of the extremogram is proposed to estimate the parameters in a max-stable space-time process. The extremogram can be viewed as the analogue of the correlogram that provides a measure of extreme dependence in both space and time. We describe some of the asymptotic properties of the resulting parameter estimates and propose subsampling procedures to obtain asymptotically correct confidence intervals. This estimation procedure will be illustrated in fitting a max-stable model to radar rainfall measurements in a region in Florida. (This is joint work with Sven Buhl, Claudia Klüppelberg, and Christina Steinkohl).
Speaker: Prof. Richard A. Davis got his Ph.D. from the University of California in 1979. After that, he has had various academic positions at universities such as M.I.T., the University of California, the University of Melbourne, the University of Copenhagen and Chalmers University of Technology. Now he is a Professor of Statistics at Columbia University. He is and has been the Editor, Advisory Editor or Associate Editor of many well-known journals, such as Bernoulli, the Journal of Business and Economic Statistics, Stochastic Processes and their Applications, and the Annals of Applied Probability. His research interests include extreme value theory, times series analysis, applied probability and stochastic processes.