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