Martin Wahl - Research

Publications

• Optimal parameter estimation for linear SPDEs from multiple measurements 
  Annals of Statistics, to appear (with A. Tiepner, R. Altmeyer)
• A note on the prediction error of principal component regression in high dimensions 
  Theory Probab. Math. Statist. 109, 37-53, 2023 (with L. Hucker)
• Functional estimation in log-concave location families 
  High dimensional probability IX—the ethereal volume, 393-440
  Birkhäuser/Springer, Cham, 2023 (with V. Koltchinskii)
• Relative perturbation bounds with applications to empirical covariance operators
  Advances in Mathematics 412, 2023 (with M. Jirak).
• Van Trees inequality, group equivariance, and estimation of principal subspaces
  Foundations of Modern Statistics. On the occasion of Volodia Spokoiny's 60th birthday, 301-321
  Springer Proc. Math. Stat., 425, Springer, Cham, 2023.
• Lower bounds for invariant statistical models with applications to principal component analysis
  Ann. Inst. Henri Poincaré Probab. Stat. 58 1565−1589, 2022.
• Nonparametric goodness-of-fit testing for parametric covariate models in pharmacometric analyses
  CPT: Pharmacometrics & Systems Pharmacology 10, 564−576, 2021
  (with N. Hartung, A. Rastogi, W. Huisinga)
• Analyzing the discrepancy principle for kernelized spectral filter learning algorithms
  Journal of Machine Learning Research 22, 1−59, 2021 (with A. Celisse)
• Statistical inference in sparse high-dimensional additive models
  Annals of Statistics 49, 1514-1536, 2021 (with K. Gregory, E. Mammen).
• High-probability bounds for the reconstruction error of PCA
  Statistics & Probability Letters 161, 2020 (with C. Milbradt)
• Perturbation bounds for eigenspaces under a relative gap condition
  Proceedings of the AMS 148, 479-494, 2020 (with M. Jirak)
• Nonasymptotic upper bounds for the reconstruction error of PCA
  Annals of Statistics 48, 1098-1123, 2020 (with M. Reiß)
• Functional estimation and hypothesis testing in nonparametric boundary models
  Bernoulli 25, 2597-2619, 2019 (with M. Reiß).
• On the mod-Gaussian convergence of a sum over primes
  Mathematische Zeitschrift 276, 635-654, 2014.

Preprints

• A kernel-based analysis of Laplacian Eigenmaps
• Quantitative limit theorems and bootstrap approximations for empirical spectral projectors (with M. Jirak)
• On the perturbation series for eigenvalues and eigenprojections
• A theory of nonparametric regression in the presence of complex nuisance components