Research Group "Stochastic Algorithms and Nonparametric Statistics"

Research Seminar "Mathematical Statistics" Winter Semester 2017/2018

  • Place: Weierstrass-Institute for Applied Analysis and Stochastics, Erhard-Schmidt-Hörsaal, Mohrenstraße 39, 10117 Berlin
  • Time: >Wednesdays, 10.00 a.m. - 12.30 p.m.
18.10.17 Prof. Dr. Vladimir Spokoiny (WIAS und HU Berlin)
Big ball probability with applications in statistical inference
We derive the bounds on the Kolmogorov distance between probabilities of two Gaussian elements to hit a ball in a Hilbert space. The key property of these bounds is that they are dimensional-free and depend on the nuclear (Schatten-one) norm of the difference between the covariance operators of the elements. We are also interested in the anticoncentration bound for a squared norm of a non-centered Gaussian element in a Hilbert space. All bounds are sharp and cannot be improved in general. We provide a list of motivation examples and applications in statistical inference for the derived results as well. (joint with Götze, Naumov and Ulyanov)
25.10.17 Debarghya Ghoshdastidar (Universität Tübingen)
Kantorovich distance based kernel for Gaussian Processes: estimation and forecast
In this work, we consider the problem of testing between two populations of inhomogeneous random graphs de ned on the same set of vertices. We are particularly interested in the high-dimensional setting where the population size is potentially much smaller than the graph size, and may even be constant. It is known that this setting cannot be tackled if the separation between two models is quanti ed in terms of total variation distance. Hence, we study two-sample testing problems where the separation between models is quanti ed by the Frobenius or operator norms of the di erence between the population adjacency matrices. We derive upper and lower bounds for the minimax separation rate for these problems. Interestingly, the proposed near-optimal tests are uniformly consistent in both the large graph, small sample and small graph, large sample regimes. This is a joint work with Maurilio Gutzeit, Alexandra Carpentier and Ulrike von Luxburg.
01.11.17 Prof. Dr. Denis Belomestny (Universität Duisburg-Essen)
08.11.17 Prof. Arnak Dalayan (ENSAE ParisTech)
15.11.17 Prof. Enkelejd Hashorva (Universität Lausanne)
Extremes Gaussian random fields, max-stable processes, scaling/aggregation of risks, Parisian ruin or price optimisation for insurance
22.11.17 We celebrate the 50th anniversary of the MMS

29.11.17 Prof. Dr. Gitta Kotyniok (TU Berlin)
06.12.17 Prof. Dr. Alexander Meister (Universität Rostock)
Nonparametric density estimation for intentionally corrupted functional data
We consider statistical models where, in order to satisfy privacy constraints, functional data are artificially contaminated by independent Wiener processes. We show that the corrupted observations have a Wiener density, which determines the distribution of the original functional random variables uniquely. We construct a nonparametric estimator of the functional density and study its asymptotic properties. We provide an upper bound on its mean integrated squared error which yields polynomial convergence rates, and we establish lower bounds on the minimax convergence rates which are close to the rates attained by our estimator. Our estimator requires the choice of a basis and of two smoothing parameters. We propose data-driven ways of choosing them and prove that the asymptotic quality of our estimator is not significantly affected by the empirical parameter selection. We apply our technique to a classification problem of real data and provide some numerical results. This talk is based on a joint work with A. Delaigle (University of Melbourne).





17.01.18 Prof. Anthony Nouy (École Centrale Nantes)

31.01.18 Prof. Elisabeth Gassiat (Université Paris-Sud)

14.02.18 Prof. Jean-Pierre Florens (Université Toulouse)

last reviewed: October 11, 2017, by Christine Schneider