Richard Nickl’s Publications Page
My research focuses on the mathematical foundations of high- and infinite dimensional inference problems in contemporary statistical science. Some of my recent interests involve a rigorous study of the Bayesian approach to inverse problems -- some of the relevant ideas can be found in this brief survey article.
[A] Mathematical foundations of infinite-dimensional statistical models. (with E. Giné). 690p., Cambridge University Press (2016).
 Bernstein - von Mises theorems for statistical inverse problems II: compound Poisson processes. (with J. Söhl). ArXiv preprint (2017)
 Efficient estimation of linear functionals of principal components. (with V. Koltchinskii, M. Löffler) arXiv preprint (2017)
 Efficient nonparametric Bayesian inference for X-ray transforms. (with F. Monard, G.P. Paternain). arXiv preprint (2017)
 Bernstein - von Mises theorems for statistical inverse problems I: Schrödinger equation. arXiv preprint (2017)
 Inference on covariance operators via concentration inequalities: k-sample tests, classification, and clustering via Rademacher complexities. (with A. Kashlak, J. Aston). arXiv preprint (2016)
 Adaptive confidence sets for matrix completion. (with A. Carpentier, O. Klopp, M. Löffler). Bernoulli, to appear
 Comments on: High-dimensional simultaneous inference with the bootstrap. (with M. Löffler). TEST 26 (2017) 731-733.
 Nonparametric Bayesian posterior contraction rates for discretely observed scalar diffusions. (with J. Söhl). Annals of Statistics 45 (2017) 1664-1693.
 High-frequency Donsker theorems for Lévy Measures. (with M. Reiß, J. Söhl, M. Trabs). Probability Theory and Related Fields 164 (2016) 61-108.
 The mathematical work of Evarist Giné. (with V. Koltchinskii, S. van de Geer, J. Wellner). Stochastic Processes and Applications (memorial issue for E. Giné) 126 (2016) 3607-3622 [Catalan translation]
 On signal detection and confidence sets in low rank inference problems. (with A. Carpentier). Electronic Journal of Statistics 9 (2015) 2675-2688.
 Uncertainty quantification for matrix compressed sensing and quantum tomography problems. (with A. Carpentier, J. Eisert, D. Gross). arXiv preprint (2015)
 Invited Discussion of: “Frequentist coverage of adaptive nonparametric Bayesian credible sets”. Annals of Statistics 43 (2015) 1429-1436.
 On the Bernstein-von Mises phenomenon for nonparametric Bayes procedures. (with I. Castillo). Annals of Statistics 42 (2014) 1941-1969.
 Confidence Sets in Sparse Regression. (with S. van de Geer). Annals of Statistics 41 (2013) 2852-2876.
 Nonparametric Bernstein-von Mises Theorems in Gaussian White Noise. (with I. Castillo). Annals of Statistics 41 (2013) 1999-2028.
 Adaptive Confidence Sets in L_2. (with A. Bull). Probability Theory and Related Fields 156 (2013) 889-919.
 Spatially Adaptive Density Estimation by Localised Haar Projections. (with F. Gach , V. Spokoiny), Annales de l’Institut Henri Poincaré (Probab. Statist.) 49 (2013) 900-914.
 A Donsker Theorem for Lévy Measures. (with M. Reiß). Journal of Functional Analysis 263 (2012) 3306-3332.
 Concentration Inequalities and Confidence Bands for Needlet Density Estimators on Compact Homogeneous Manifolds. (with G. Kerkyacharian, D. Picard). Probability Theory and Related Fields 153 (2012) 363-404.
 Rates of Contraction for Posterior Distributions in L_r-metrics, 1 ≤r≤∞. (with E. Giné). Annals of Statistics 39 (2011) 2883-2911.
 On Adaptive Inference and Confidence Bands. (with M. Hoffmann). Annals of Statistics 39 (2011) 2383-2409.
 Global Uniform Risk Bounds for Wavelet Deconvolution Estimators. (with K. Lounici). Annals of Statistics 39 (2011) 201-231.
 Adaptive Estimation of the Distribution Function and its Density in Sup-Norm Loss by Wavelet and Spline Projections. (with E. Giné). Bernoulli 16 (2010) 1137-1163.
 Efficient Simulation-Based Minimum Distance Estimation and Indirect Inference. (with B.M. Pötscher). Mathematical Methods of Statistics 19 (2010) 327-364.
 Confidence Bands in Density Estimation. (with E. Giné). Annals of Statistics 38 (2010) 1122-1170.
 Uniform Limit Theorems for Wavelet Density Estimators. (with E. Giné). Annals of Probability 37 (2009) 1605-1646.
 An Exponential Inequality for the Distribution Function of the Kernel Density Estimator, with Applications to Adaptive Estimation. (with E. Giné). Probability Theory and Related Fields 143 (2009) 569-596.
 On Convergence and Convolutions of Random Signed Measures. Journal of Theoretical Probability 22 (2009) 38-56.
 Uniform Central Limit Theorems for Sieved Maximum Likelihood and Trigonometric Series Estimators on the Unit Circle. In: High Dimensional Probability V: The Luminy Volume (eds. C. Houdré, V. Koltchinskii, D. Mason, M. Peligrad) IMS Collections 5 (2009) 338-356.
 Adaptation on the Space of Finite Signed Measures. (with E. Giné). Mathematical Methods of Statistics 17 (2008), 113-122.
 A Simple Adaptive Estimator of the Integrated Square of a Density. (with E. Giné). Bernoulli 14 (2008), 47-61.
 Uniform Central Limit Theorems for Kernel Density Estimators. (with E. Giné). Probability Theory and Related Fields 141 (2008), 333-387.
 Donsker-Type Theorems for Nonparametric Maximum Likelihood Estimators. Probability Theory and Related Fields 138 (2007), 411-449.
 Bracketing Metric Entropy Rates and Empirical Central Limit Theorems for Function Classes of Besov- and Sobolev-Type. (with B.M. Pötscher). Journal of Theoretical Probability, 20 (2007), 177-199.
 Empirical and Gaussian Processes on Besov classes. In: High Dimensional Probability IV, (eds. E. Giné, V. Koltchinskii, W. Li, J. Zinn). IMS Lecture Notes 51 (2006), 185-195.