prof.dr. A.J. Schmidt-Hieber (Johannes)

Full Professor
EEMCS-AM-MOR
Zilverling 2057
a.j.schmidt-hieber@utwente.nl
+31534896958
Business card

Since 2018, Johannes Schmidt-Hieber is professor of statistics at the University of Twente. Click here here to access the personal webpage.

Expertise

  • Economics, Econometrics and Finance

    • Measure of Dispersion
    • Estimation Theory
    • Information

  • Mathematics

    • Bounds
    • Gaussian Process
    • Parameters
    • Bayesian
    • Number

Organisations

Articles

  1. Bayesian variance estimation in the Gaussian sequence model with partial information on the means preprint 
    With Gianluca Finocchio.
  2. Posterior consistency for n in the binomial (n,p) problem with both parameters unknown - with applications to quantitative nanoscopy. preprint 
    With Laura Schneider, Thomas Staudt, Andrea Krajina, Timo Aspelmeier and Axel Munk.
  3. Posterior contraction rates for support boundary recovery preprint 
    With Markus Reiss.
  4. Nonparametric regression using deep neural networks with ReLU activation function preprint 
    To appear as a discussion article in the Annals of Statistics
  5. Tests for qualitative features in the random coefficients model preprint 
    With Fabian Dunker, Konstantin Eckle, and Katharina Proksch. 
    To appear in Electronic Journal of Statistics
  6. Nonparametric Bayesian analysis of the compound Poisson prior for support boundary recovery preprint 
    With Markus Reiss. 
    To appear in Annals of Statistics
  7. Asymptotic nonequivalence of density estimation and Gaussian white noise for small densities preprint 
    With Kolyan Ray. 
    To appear in Annales de l'Institut Henri Poincaré B.
  8. A comparison of deep networks with ReLU activation function and linear spline-type methods pdf 
    Neural Networks, Volume 110, 232-242, 2019. 
    With Konstantin Eckle.
  9. The Le Cam distance between density estimation, Poisson processes and Gaussian white noise article preprint 
    Mathematical Statistics and Learning. Volume 1, Issue 2, 101-170, 2018. With Kolyan Ray.
  10. A regularity class for the roots of non-negative functions. pdf arXiv 
    Annali di Matematica Pura ed Applicata. Volume 196, Number 6, 2091-2103, 2017. With Kolyan Ray.
  11. Minimax theory for a class of non-linear statistical inverse problems. article revised preprint 
    Inverse Problems. Volume 32, Number 6, 065003, 2016. With Kolyan Ray.
  12. Conditions for posterior contraction in the sparse normal means problem. pdf 
    Electronic Journal of Statistics. Volume 10, Number 1, 976-1000, 2016. With Stéphanie van der Pas and JB Salomond.
  13. Bayesian linear regression with sparse priors. pdf arXiv 
    Annals of Statistics. Volume 43, Number 5, 1986-2018, 2015. With Ismael Castillo and Aad van der Vaart.
  14. On adaptive posterior concentration rates. pdf 
    Annals of Statistics. Volume 43, Number 5, 2259-2295, 2015. With Marc Hoffmann and Judith Rousseau.
  15. Spot volatility estimation for high-frequency data: adaptive estimation in practice. pdf arXiv 
    Springer Lecture Notes in Statistics: Modeling and Stochastic Learning for Forecasting in High Dimension. 213-241, 2015. With Till Sabel and Axel Munk.
  16. Asymptotic equivalence for regression under fractional noise. pdf arXiv 
    Annals of Statistics, Volume 42, Number 6, 2557-2585, 2014.
  17. Asymptotically efficient estimation of a scale parameter in Gaussian time series and closed-form expressions for the Fisher information. pdf arXiv supplement 
    Bernoulli, Volume 20, Number 2, 747-774, 2014. With Till Sabel.
  18. On an estimator achieving the adaptive rate in nonparametric regression under Lp-loss for all 1≤p≤∞. preprint 
    This is an update of the working paper  pdf. In the first version, we only consider simultaneous adaptation with respect to L2- and L∞-loss. This article might be easier to read and includes a small numerical study.
  19. Multiscale methods for shape constraints in deconvolution: Confidence statements for qualitative features.pdfsupplement 
    Annals of Statistics, Volume 41, Number 3, 1299-1328, 2013. With Axel Munk and Lutz Dümbgen. 
    A first draft of this paper appeared under the title: "Multiscale methods for shape constraints in deconvolution" in 2011.pdf. It contains essentially the same results, but under a very strong assumption on the decay of the Fourier transform of the error density. The first version is much easier to read and does not require the theory of pseudo-differential operators.
  20. Adaptive wavelet estimation of the diffusion coefficient under additive error measurements. pdf software 
    Annales de l'Institut Henri Poincaré, 48, 1186-1216. With Marc Hoffmann and Axel Munk. 
    An earlier version of this paper was published as a working paper under the title "Nonparametric estimation of the volatility under microstructure noise: wavelet adaptation." pdf.
  21. Nonparametric methods in spot volatility estimation. pdf 
    Dissertation. Universität Göttingen und Universtät Bern, 2010.
  22. Lower bounds for volatility estimation in microstructure noise models. pdf 
    Borrowing Strength: Theory Powering Applications - A Festschrift for Lawrence D. Brown, IMS Collections, 6, 43-55, 2010. With Axel Munk.
  23. Nonparametric estimation of the volatility function in a high-frequency model corrupted by noise. pdf 
    Electronic Journal of Statistics, 4, 781-821, 2010. With Axel Munk.
  24. Sharp minimax estimation of the variance of Brownian motion corrupted with Gaussian noise. pdf (including supplementary material). 
    Statistica Sinica, 20, 1011-1024, 2010 . With T. Tony Cai and Axel Munk.

Publications

2024
Convergence guarantees for forward gradient descent in the linear regression model, Article 106174. Bos, T. & Schmidt-Hieber, J.https://doi.org/10.1016/j.jspi.2024.106174Lower bounds for the trade-off between bias and mean absolute deviation, Article 110182. Derumigny, A. & Schmidt-Hieber, J.https://doi.org/10.1016/j.spl.2024.110182Local convergence rates of the nonparametric least squares estimator with applications to transfer learning, 1845-1877. Schmidt-Hieber, J. & Zamolodtchikov, P.https://doi.org/10.3150/23-BEJ1655Codivergences and information matrices, 253-282. Derumigny, A. & Schmidt-Hieber, J.https://doi.org/10.1007/s41884-024-00135-2
2023
On lower bounds for the bias-variance trade-off, 1510 - 1533. Derumigny, A. & Schmidt-Hieber, A. J.https://doi.org/10.1214/23-AOS2279Posterior Contraction for Deep Gaussian Process Priors, 1-49. Finocchio, G. & Schmidt-Hieber, A. J.https://jmlr.org/papers/volume24/21-0556/21-0556.pdfOn Generalization Bounds for Deep Networks Based on Loss Surface Implicit Regularization, 1203- 1223. Imaizumi, M. & Schmidt-Hieber, A. J.https://doi.org/10.1109/TIT.2022.3215088
2022
Local convergence rates of the least squares estimator with applications to transfer learning. ArXiv.org. Schmidt-Hieber, J. & Zamolodtchikov, P.https://doi.org/10.48550/arXiv.2204.05003Convergence rates of deep ReLU networks for multiclass classification, 2724 - 2773. Bos, T. & Schmidt-Hieber, A. J.https://doi.org/10.1214/22-EJS2011
2021
Posterior analysis of n in the binomial (n,p) problem with both parameters unknown—with applications to quantitative nanoscopy, 3534-3558. Schmidt-Hieber, A. J., Schneider, L., Staudt, T., Krajina, A., Aspelmeier, T. & Munk, A.https://doi.org/10.1214/21-AOS2096Two perspectives on high-dimensional estimation problems: posterior contraction and median-of-means. University of Twente. Finocchio, G.https://doi.org/10.3990/1.9789036552356Posterior contraction for deep Gaussian process priors. Finocchio, G. & Schmidt-Hieber, A. J.https://arxiv.org/abs/2105.07410The Kolmogorov–Arnold representation theorem revisited, 119-126. Schmidt-Hieber, A. J.https://doi.org/10.1016/j.neunet.2021.01.020
2020
Posterior contraction rates for support boundary recovery, 6638. Reiss, M. & Schmidt-Hieber, J.https://doi.org/10.1016/j.spa.2020.06.005Nonparametric Bayesian analysis of the compound Poisson prior for support boundary recovery, 1432-1451. Reiss, M. & Schmidt-Hieber, A. J.https://doi.org/10.1214/19-AOS1853Rejoinder: “Nonparametric regression using deep neural networks with ReLU activation function”, 1916-1921. Schmidt-Hieber, A. J.https://doi.org/10.1214/19-AOS1931Nonparametric regression using deep neural networks with ReLU activation function, 1875-1897. Schmidt-Hieber, A. J.https://doi.org/10.1214/19-AOS1875On lower bounds for the bias-variance trade-off. ArXiv.org. Derumigny, A. & Schmidt-Hieber, J.https://arxiv.org/abs/2006.00278Ein Beitrag zur Statistischen Theorie des Deep Learnings. Verlag Dr. Hut. Langer, S.Bayesian variance estimation in the Gaussian sequence model with partial information on the means, 239-271. Finocchio, G. & Schmidt-Hieber, J.https://doi.org/10.1214/19-EJS1671

Research profiles

Address

University of Twente

Zilverling (building no. 11), room 2057
Hallenweg 19
7522 NH Enschede
Netherlands

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