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.
Book
[A] Mathematical foundations of infinitedimensional statistical models. (with E. Giné). 690p., Cambridge University Press (2016).
Papers
[37] Bernstein  von Mises theorems for statistical inverse problems II: compound Poisson processes. (with J. Söhl). ArXiv preprint (2017)
[36] Efficient estimation of linear functionals of principal components. (with V. Koltchinskii, M. Löffler) arXiv preprint (2017)
[35] Efficient nonparametric Bayesian inference for Xray transforms. (with F. Monard, G.P. Paternain). arXiv preprint (2017)
[34] Bernstein  von Mises theorems for statistical inverse problems I: Schrödinger equation. arXiv preprint (2017)
[33] Inference on covariance operators via concentration inequalities: ksample tests, classification, and clustering via Rademacher complexities. (with A. Kashlak, J. Aston). arXiv preprint (2016)
[32] Adaptive confidence sets for matrix completion. (with A. Carpentier, O. Klopp, M. Löffler). Bernoulli, to appear
[31] Comments on: Highdimensional simultaneous inference with the bootstrap. (with M. Löffler). TEST 26 (2017) 731733.
[30] Nonparametric Bayesian posterior contraction rates for discretely observed scalar diffusions. (with J. Söhl). Annals of Statistics 45 (2017) 16641693.
[29] Highfrequency Donsker theorems for Lévy Measures. (with M. Reiß, J. Söhl, M. Trabs). Probability Theory and Related Fields 164 (2016) 61108.
[28] A sharp adaptive confidence ball for selfsimilar functions. (with B. Szabó). Stochastic Processes and Applications (memorial issue for E. Giné) 126 (2016) 39133934.
[27] 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) 36073622 [Catalan translation]
[26] On signal detection and confidence sets in low rank inference problems. (with A. Carpentier). Electronic Journal of Statistics 9 (2015) 26752688.
[25] Uncertainty quantification for matrix compressed sensing and quantum tomography problems. (with A. Carpentier, J. Eisert, D. Gross). arXiv preprint (2015)
[24] Invited Discussion of: “Frequentist coverage of adaptive nonparametric Bayesian credible sets”. Annals of Statistics 43 (2015) 14291436.
[23] On the Bernsteinvon Mises phenomenon for nonparametric Bayes procedures. (with I. Castillo). Annals of Statistics 42 (2014) 19411969.
[22] Confidence Sets in Sparse Regression. (with S. van de Geer). Annals of Statistics 41 (2013) 28522876.
[21] Nonparametric Bernsteinvon Mises Theorems in Gaussian White Noise. (with I. Castillo). Annals of Statistics 41 (2013) 19992028.
[20] Adaptive Confidence Sets in L_2. (with A. Bull). Probability Theory and Related Fields 156 (2013) 889919.
[19] Spatially Adaptive Density Estimation by Localised Haar Projections. (with F. Gach , V. Spokoiny), Annales de l’Institut Henri Poincaré (Probab. Statist.) 49 (2013) 900914.
[18] A Donsker Theorem for Lévy Measures. (with M. Reiß). Journal of Functional Analysis 263 (2012) 33063332.
[17] 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) 363404.
[16] Rates of Contraction for Posterior Distributions in L_rmetrics, 1 ≤r≤∞. (with E. Giné). Annals of Statistics 39 (2011) 28832911.
[15] On Adaptive Inference and Confidence Bands. (with M. Hoffmann). Annals of Statistics 39 (2011) 23832409.
[14] Global Uniform Risk Bounds for Wavelet Deconvolution Estimators. (with K. Lounici). Annals of Statistics 39 (2011) 201231.
[13] Adaptive Estimation of the Distribution Function and its Density in SupNorm Loss by Wavelet and Spline Projections. (with E. Giné). Bernoulli 16 (2010) 11371163.
[12] Efficient SimulationBased Minimum Distance Estimation and Indirect Inference. (with B.M. Pötscher). Mathematical Methods of Statistics 19 (2010) 327364.
[11] Confidence Bands in Density Estimation. (with E. Giné). Annals of Statistics 38 (2010) 11221170.
[10] Uniform Limit Theorems for Wavelet Density Estimators. (with E. Giné). Annals of Probability 37 (2009) 16051646.
[9] 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) 569596.
[8] On Convergence and Convolutions of Random Signed Measures. Journal of Theoretical Probability 22 (2009) 3856.
[7] 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) 338356.
[6] Adaptation on the Space of Finite Signed Measures. (with E. Giné). Mathematical Methods of Statistics 17 (2008), 113122.
[5] A Simple Adaptive Estimator of the Integrated Square of a Density. (with E. Giné). Bernoulli 14 (2008), 4761.
[4] Uniform Central Limit Theorems for Kernel Density Estimators. (with E. Giné). Probability Theory and Related Fields 141 (2008), 333387.
[3] DonskerType Theorems for Nonparametric Maximum Likelihood Estimators. Probability Theory and Related Fields 138 (2007), 411449.
[2] Bracketing Metric Entropy Rates and Empirical Central Limit Theorems for Function Classes of Besov and SobolevType. (with B.M. Pötscher). Journal of Theoretical Probability, 20 (2007), 177199.
[1] 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), 185195.