Topics of Research in the mathematical statistics group

Examples of pointwise testing on a continuous domain (Left: for the cumulative distribution function being identity. Right: for the intensity of a Poisson process) Green are correct pointwise rejections, red incorrect. The a priori bound on the expected volume ratio incorrect/total rejected is set to 0.4.

Reference: G. Blanchard, S. Delattre, E. Roquain, E. : Testing over a continuum of null hypotheses with False Discovery Rate control. Bernoulli 20, 303-334 (2014)

Topics of Research: 

• Machine learning
  • Classification and discrimination
  • Statistical Learning theory
  • (Reproducing) kernel methods
  • Boosting methods
  • Decontamination models
  • Model selection
• Multiple testing procedures
  • FWER and FDR control
  • Adaptation to unknown covariance structures
  • Permutation and bootstrap methods
• Statistical Inverse Problems 
  • Optimal regularization for statistical inverse problems
  • Conjugate gradient methods
  • Early stopping methods
• Nonparametric Curve Estimation
  • Nonparametric estimators for densities, regression functions, conditional variances, conditional U-statistics and hazard functions and their asymptotic properties (consistency, limit distributions)
  • Application of limit theorems for the construction of asymptotic goodness-of-fit tests and confidence bands
• Estimating and Testing in Survival Analysis
  • Estimation in the proportional hazards model
  • Testing in the accelerated life time model
  • Resampling procedures for survival models
  • The hazard rate in models with covariates
• Estimating and Testing in Sparse Multinomial Data Sets
  • Testing independence in sparse contingency tables
  • Goodness-of-Fit-Tests in Sparse Multinomial Data Sets