Nonparametric and multivariate statistics

Group leader: Prof. Dr. Lutz Dümbgen

Every now and then, we are looking at the foundations of stochastics. For instance, we derive new probability inequalities [1], work on exact confidence bounds or try to look at traditional methods from a new point of view [2]. Another line of research is empirical processes and nonparametric statistics, e.g. [3]. In particular, statistical inference under shape constraints is a recurring topic, e.g. [4, 5]. Roughly speaking, shape constraints on density or regression functions are an interesting alternative to simpler but sometimes too idealistic parametric models, and they are less ad hoc than quantitative smoothness assumptions or regularization approaches. A third line of research is multivariate statistics, where we propose new methods [6, 7] or algorithms [8].

Current collaborators from abroad include Jon A. Wellner (University of Washington, Seattle, USA) and Klaus Nordhausen (University of Jyväskylä, Finland).

Selected publications

  1. L. Dümbgen, R.J. Samworth and A. Wellner (2021). Bounding distributional errors via density ratios. Bernoulli 27(2), 818-852. [DOI:10.3150/20-BEJ1256]
  2. L. Dümbgen and L. Davies (2020). Connecting model-based and model-free approaches to linear least squares regression. [arXiv:abs/1807.09633]
  3. L. Dümbgen and J.A. Wellner (2021). A new approach to tests and confidence bands for distribution functions. [arXiv:abs/1402.2918]
  4. L. Dümbgen, P. Kolesnyk and R.A. Wilke (2017). Bi-log-concave distribution functions. Journal of Statistical Planning and Inference 184, 1-17. [DOI:10.1016/j.jspi.2016.10.005]
  5. A. Mösching and L. Dümbgen (2020). Monotone least squares and isotonic quantiles. Electronic Journal of Statistics 14(1), 24-49. [DOI:10.1214/19-EJS1659]
  6. L. Dümbgen, B.-W. Igl and A. Munk (2008). P-values for classification. Electronic Journal of Statistics 2, 468-493. [DOI:10.1214/08-EJS245]
  7. D.E. Tyler, F. Critchley, L. Dümbgen and H. Oja (2009). Invariant co-ordinate selection (with discussion). Journal of the Royal Statistical Society, Series B 71(3), 549-592. [DOI:10.1111/j.1467-9868.2009.00706.x]
  8. L. Dümbgen, K. Nordhausen and H. Schuhmacher (2016). New algorithms for M-estimation of multivariate scatter and location. Journal of Multivariate Analysis 144, 200-217. [DOI:10.1016/j.jmva.2015.11.009]

Group members

Former members

  • Dr. Alexandre Mösching
  • Dr. Christof Strähl
  • Dr. Niki R. Zumbrunnen
  • Dr. Dirk Klingbiel
  • Dr. Angelika Rohde
  • Dr. Kaspar Rufibach
  • Dr. Bernd-Wolfgang Igl
  • Dr. Sandra Freitag-Wolf