FOR 916:  Statistical Regularisation and Qualitative Constraints - Inference, Algorithms, Asymptotics and Applications

Final Report Abstract

A basic challenge for statistics at the interface of different sciences is the development of methods for the analysis of massive data sets, complex data structures and highdimensional predictors. The objectives of this German-Swiss research group have been specific development and analysis of statistical regularization methods for such complex data structures as they occur in different fields of application. In the foreground, there are methods in which regularization is given by qualitative constraints on the structure or geometry of data models. Our basic paradigm is that statistical regularization by qualitative constraints produces a consistent methodology for modeling of data structures which, on the one hand, is flexible enough to identify and scientifically utilize main structural features of data, but, on the other hand, specific enough to control prediction and classification error. The major findings of this research unit can be summarised as follows: Statistical regularization with structural or qualitative constraints provides a coherent statistical and computational perspective and solution strategy for extracting relevant information from complex data. This bridges and unifies various challenging issues in the subject fields of econometrics, biophysics and socioeconomics.

Publications

• (2015). M -functionals of multivariate scatter. Statistics Surveys 9, 32–105
  L. Dümbgen, M. Pauly and T. Schweizer
  
• (2015). Quantile regression methods. Emerging Trends in the Social and Behavioral Sciences (eds.) Robert Scott and Stephen Kosslyn, Hoboken, NJ: John Wiley and Sons
  B. Fitzenberger and R. A. Wilke
  
• Goodness-of-fit tests based on series estimators in nonparametric instrumental regression. J. of Econometrics, 184, 328–346, 2015
  C. Breunig
  
• Jointly interventional and observational data: estimation of interventional Markov equivalence classes of directed acyclic graphs. Journal of the Royal Statistical Society, Series B, 77 (1):291–318, 2015
  A. Hauser and P. Buhlmann
  
• Multiscale DNA partitioning: statistical evidence for segments. Bioinformatics, 30(16):2255-62, 2015
  A. Futschik, T. Hotz, A. Munk and H. Sieling
  
• On various confidence intervals post-modelselection. Statistical Science, 30: 216–227, 2015
  H. Leeb and B.M. Pötscher and K. Ewald
  
• Spot volatility estimation for high-frequency data: adaptive estimation in practice. In: Antoniadis A., Poggi JM., Brossat X. (eds) Modeling and Stochastic Learning for Forecasting in High Dimensions. Lecture Notes in Statistics, vol 217. Springer, Cham, 2015
  T. Sabel, J. Schmidt-Hieber, and A. Munk
  
• (2016). New algorithms for M -estimation of multivariate scatter and location. Journal of Multivariate Analysis 144, 200–217
  L. Dümbgen, K. Nordhausen and H. Schuhmacher
  
• (2016). pvclass: An R package for p-values for classification. Journal of Statistical Software 39
  N. Zumbrunnen, and L. Dümbgen
  
• Confidence sets based on thresholding estimators in high-dimensional Gaussian regression. Econometric Reviews, 35(8-10):1412-1455, 2016
  U. Schneider
  
• Partial least squares for dependent data. Biometrika, 2016
  M. Singer, T. Krivobokova, A. Munk and B.L. de Groot
  
• (2017). Competing risks quantile regression at work: In-depth exploration of the role of public child support for the duration of maternity leave. Journal of Applied Statistics, 44(1):109-122
  S. Dlugosz, S. M. S. Lo, R.A. Wilke
  

Projects