Johannes Schmidt-Hieber

Professor of statistics at the University of Twente

Visiting addresses:
Zilverling Building, Room 4058
Drienerlolaan 5
7522 NB Enschede


We soon have more job openings for PhD and postdoc positions in our group. If you have a background in statistics/probability/mathematics feel free to send an email to .

  1. Convergence rates of deep ReLU networks for multiclass classification preprint
    With Thijs Bos
  2. Posterior contraction for deep Gaussian process priors preprint
    With Gianluca Finocchio
  3. On lower bounds for the bias-variance trade-off preprint
    With Alexis Derumigny
  4. The Kolmogorov-Arnold representation theorem revisited article
    Neural Networks, Volume 137, 119-126, 2021.
  5. On frequentist coverage of Bayesian credible sets for estimation of the mean under constraints preprint
    With Kevin Duisters
    To appear as book chapter within Springer IISA series on Statistics and Data Science.
  6. Deep ReLU network approximation of functions on a manifold. preprint
  7. 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.
    Annals of Statistics, to appear.
  8. Posterior contraction rates for support boundary recovery preprint article
    Stochastic Processes and their Applications, Volume 130, Issue 11, 6638-6656, 2020. With Markus Reiss.
  9. Nonparametric regression using deep neural networks with ReLU activation function article pdf preprint
    Annals of Statistics, Volume 48, Number 4, 1875-1897, 2020.
    This article has been discussed by
  10. Rejoinder: "Nonparametric regression using deep neural networks with ReLU activation function" article pdf
    Annals of Statistics, Volume 48, Number 4, 1916-1921, 2020.
  11. Nonparametric Bayesian analysis of the compound Poisson prior for support boundary recovery article pdf preprint
    Annals of Statistics, Volume 48, Number 3, 1432-1451, 2020. With Markus Reiss.
  12. Bayesian variance estimation in the Gaussian sequence model with partial information on the means. article
    Electronic Journal of Statistics, Volume 14, Number 1, 239-271, 2020. With Gianluca Finocchio.
  13. Asymptotic nonequivalence of density estimation and Gaussian white noise for small densities preprint article
    Annales de l'Institut Henri Poincaré B, Volume 55, Number 4, 2195-2208, 2019. With Kolyan Ray.
  14. Tests for qualitative features in the random coefficients model pdf
    Electronic Journal of Statistics, Volume 3, 2257-2306, 2019. With Fabian Dunker, Konstantin Eckle, and Katharina Proksch.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. On adaptive posterior concentration rates. pdf
    Annals of Statistics. Volume 43, Number 5, 2259-2295, 2015. With Marc Hoffmann and Judith Rousseau.
  22. 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.
  23. Asymptotic equivalence for regression under fractional noise. pdf arXiv
    Annals of Statistics, Volume 42, Number 6, 2557-2585, 2014.
  24. 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.
  25. On an estimator achieving the adaptive rate in nonparametric regression under L p -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 L 2 - and L -loss. This article might be easier to read and includes a small numerical study.
  26. Multiscale methods for shape constraints in deconvolution: Confidence statements for qualitative features.pdf supplement
    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.
  27. 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.
  28. Nonparametric methods in spot volatility estimation. pdf
    Dissertation. Universität Göttingen und Universtät Bern, 2010.
  29. 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.
  30. 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.
  31. 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.
  1. Statistical theory for deep neural networks with ReLU activation function. pdf
    Oberwolfach Reports, 2018.
  2. Nonparametric Bayes for an irregular model. pdf
    Oberwolfach Reports, 2017.
  3. Asymptotic equivalence for regression under dependent noise. pdf
    Oberwolfach Reports, 2015.
  4. Reconstruction of risk measures from financial data. pdf
    Nieuw Archief voor Wiskunde, 2014.
  5. Simultaneously adaptive estimation for L 2 - and L -loss. pdf
    Oberwolfach Reports,2014.
  6. Detection of qualitative features in statistical inverse problems. pdf
    Oberwolfach Reports, 2012.
  7. Obtaining qualitative statements in deconvolution models. pdf
    Oberwolfach Reports, 2012.
  8. The Estimation of different scales in microstructure noise models from a nonparametric regression perspective. pdf
    Oberwolfach Reports, 2009. With Axel Munk.

Curriculum Vitae:
Born 1984 in Freiburg im Breisgau, Germany. Studies in mathematics at Universität Freiburg (2003-2004) and Universität Göttingen (2004-2007). PhD studies at Universität Göttingen and Universität Bern 2007- 2011 (supervisors: Axel Munk and Lutz Dümbgen). Postdoc at Vrije Universiteit Amsterdam and ENSAE, Paris. Assistant professor at Leiden University (2014-2018). Since 2018, full professor at University of Twente.

Abitur 2004; Diploma in mathematics with minor theoretical physics, Universität Göttingen, 2007. Dissertation, Universität Göttingen and Universität Bern 2011 (double degree program, summa cum laude).

Research Experience:
Visiting Scholar at University of California, Davis (September 2006-March 2007); Research stays at Wharton Business school, Philadelphia (February 2008), RICAM, Linz (October-November 2008), ENSAE, Paris (August and December 2009, June 2012-May 2013, January 2019), Vrije Universiteit Amsterdam (June 2011-May 2012), Universität Heidelberg (December 2010), Humboldt University (August 2014, August 2016, January- March 2018), Paris Dauphine (February 2014), SAMSI (June 2015), Göttingen (October-December 2015), Bochum (June-July 2016), Fudan university (June, August 2017), Isaac Newton institute (January-June 2018), Simons Institute Berkeley (July 2019). Guest of Collaborative Research Center 649 at Humboldt University Berlin (2010 - 2011).

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Awards and grants: Conference organization: Other activities:

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