Event
Empirical Process Theory Through Examples| Title of the event | Empirical Process Theory Through Examples |
| Series | Stochastisches Kolloquium |
| Organizer | Institut für Mathematische Stochastik |
| Speaker | Prof. Dr. Bodhisattva Sen |
| Speaker institution | Columbia University, New York |
| Type of event | Kolloquium |
| Category | Forschung |
| Registration required | Nein |
| Details | Abstract: In the talk I will briefly describe three problems from my research where empirical process theory turns out to be crucial. In the first example I consider the nonparametric maximum likelihood estimator (NPMLE) of a decreasing density on the positive half-line. I will illustrate how the weak convergence of the usual empirical process is useful in deriving the pointwise limiting distribution of the NPMLE. In the second example I consider the least squares estimator (LSE) of an unknown multivariate convex regression function. I will illustrate how metric entropy and chaining, two fundamental concepts in the empirical process theory, can be used to provide risk (upper) bounds for the LSE. In the third problem I shall consider estimation of the optimal transport map between two multivariate (continuous) distributions given i.i.d. samples. I will show how one can derive the rate of convergence of the estimated transport map using tools from empirical process theory. In all the three problems I will try to emphasize the main ideas and only provide proof sketches. |
| Date | Start: 09.07.2021, 16:15 Uhr Ende: 09.07.2021 , 17:45 Uhr |
| Location | BBB/Zoom |
| Contact |
Dr. Tobias Kley tobias.kley@uni-goettingen.de |