Preprints

• Magra, A., van der Vaart, A.W. and van Zanten, J.H. (2024).
  Semiparametric Bernstein-von Mises in linear inverse problems.
  

Published papers

2023

• Vuursteen, L., Szabo, B., van der Vaart, A.W. and van Zanten, J.H. (2023).
  Optimal testing using combined test statistics across independent studies.
  Advances in Neural Information Processing Systems (NeurIPS).
• Silvestrin, L., Hoogendoorn, M., Koole, G. and van Zanten, J.H. (2023).
  Transfer learning across datasets with different input dimensions: An algorithm and analysis for the linear regression case.
  Journal of Computational Mathematics and Data Science 9, 100086.
• Nieman, D., Szabo, B.T. and van Zanten, J.H. (2023).
  Uncertainty quantification for sparse spectral variational approximations in Gaussian process regression.
  Electronic Journal of Statistics 17(2), 2250--2288.
• Szabo, B.T., Vuursteen, L. and van Zanten, J.H. (2023).
  Optimal high-dimensional and nonparametric distributed testing under communication constraints.
  Annals of Statistics 51(3), 909--934.

2022

• Szabo, B.T. and van Zanten, J.H. (2022).
  Distributed function estimation: adaptation using minimal communication.
  Mathematical Statistics and Learning 5(3/4), 159--199.
• Nieman, D., Szabo, B.T. and van Zanten, J.H. (2022).
  Contraction rates for sparse variational approximations in Gaussian process regression.
  Journal of Machine Learning Research 23(205), 1--26.
• Szabo, B.T., Vuursteen, L. and van Zanten, J.H. (2022).
  Optimal distributed composite testing in high-dimensional Gaussian models with 1-bit communication.
  IEEE Transactions on Information Theory 68(6), 4070--4084.

2021

• Hartog, J. and van Zanten, J.H. (2021).
  Nonparametric Bayesian label prediction on a large graph using truncated Laplacian regularization. Communications in Statistics – Simulation and Computation 50(12), 3821--383.

2020

• Szabo, B.T. and van Zanten, J.H. (2020).
  Adaptive distributed methods under communication constraints. Ann. Statist. 48, no. 4, 2347–2380.

2019

• Szabo, B.T. and van Zanten, J.H. (2019).
  An asymptotic analysis of distributed nonparametric methods. J. Mach. Learn. Res. 20, 1–30.

2018

• Kirichenko, A. and van Zanten, J.H. (2018).
  Minimax lower bounds for function estimation on graphs. Electron. J. Stat. 12(1), 651-666.
• Hartog, J. and van Zanten, J.H. (2018).
  Nonparametric Bayesian label prediction on a graph.
  Comput. Statist. Data Anal., 120, 111–131.

2017

• van der Meulen, F., Schauer, M., van Zanten, J.H. (2017).
  Guided proposals for simulating multi-dimensional diffusion bridges.
  Bernoulli 23(4A), 2917–2950.
• Kirichenko, A., van Zanten, J.H. (2017).
  Estimating a smooth function on a large graph by Bayesian Laplacian regularisation.
  Electron. J. Stat. 11(1), 891–915.
• van Waaij, J. and van Zanten, J.H. (2017).
  Full adaptation to smoothness using randomly truncated series priors with Gaussian coefficients and inverse gamma scaling.
  Statist. Probab. Lett. 123, 93–99.

2016

• Knapik, B.T., Szabo, B.T., van der Vaart, A.W., van Zanten J.H. (2016).
  Bayes procedures for adaptive inference in nonparametric inverse problems.
  Probab. Theory Related Fields, 164, no.3, 771–813
• van Waaij, J. and van Zanten, J.H. (2016).
  Gaussian process methods for one-dimensional diffusions: optimal rates and adaptation.
  Electron. J. Stat. 10, 628–645.
• Sjerps, M.J., Alberink, I., Bolck, A., Stoel, R.D., Vergeer, P. and Van Zanten, J.H. (2016).
  Uncertainty and LR: to integrate or not to integrate, that's the question.
  Law, Probability and Risk 15, no. 1, 23–29.

2015

• Kirichenko, A., van Zanten, J.H. (2015).
  Optimality of Poisson processes intensity learning with Gaussian processes.
  J. Mach. Learn. Res. 16, 2909–2919.
• Szabo, B.T., van der Vaart, A.W., van Zanten J.H. (2015).
  Honest Bayesian confidence sets for the L2-norm.
  J. Statist. Plann. Inference 166, 36–51.
• Belitser, E., Serra, P., van Zanten, J.H. (2015).
  Rate-optimal Bayesian intensity smoothing for inhomogeneous Poisson processes.
  J. Statist. Plann. Inference 166, 24–35.
• Szabo, B.T., van der Vaart, A.W., van Zanten J.H. (2015).
  Rejoinder to discussions of “Frequentist coverage of adaptive nonparametric Bayesian credible sets”.
  Ann. Statist. 43, no. 4, 1463–1470.
• Szabo, B.T., van der Vaart, A.W., van Zanten J.H. (2015).
  Frequentist coverage of adaptive nonparametric Bayesian credible sets.
  Ann. Statist. 43, no. 4, 1391–1428.

2014

• Buishand, A., Jongbloed, G., Klein-Tank, A., Roth, M, Van Zanten, J.H. (2014).
  Projections of precipitation extremes based on a regional, non-stationary peaks-over-threshold approach: A case study for the Netherlands and north-western Germany.
  Weather and Climate Extremes 4, 1-10.
• van der Meulen, F., Schauer, M., van Zanten, J.H. (2014).
  Reversible jump MCMC for nonparametric drift estimation for diffusion processes.
  Comput. Statist. Data Anal. 71, 615-632.

2013

• Belitser, E., Serra, P., van Zanten, J.H. (2013).
  Estimating the period of a cyclic non-homogeneous Poisson process.
  Scand. J. Statist. 40, no. 2, 204-218.
• van Zanten J.H. (2013).
  Nonparametric Bayesian methods for one-dimensional diffusion models.
  Math. Biosci. 243, no. 2, 215-222.
• Szabo, B.T., van der Vaart, A.W., van Zanten J.H. (2013).
  Empirical Bayes scaling of Gaussian priors in the white noise model.
  Electron. J. Stat. 7, 991-1018.
• Knapik, B., van der Vaart, A.W., van Zanten, J.H. (2013).
  Bayesian recovery of the initial condition for the heat equation.
  Comm. Statist. Theory Methods 42, 1294-1313.
• De Jonge, R., van Zanten, J.H. (2013).
  Semiparametric Bernstein-Von Mises for the error standard deviation.
  Electron. J. Stat. 7, 217-243.
• van der Meulen, F., van Zanten, J.H. (2013).
  Consistent nonparametric Bayesian inference for discretely observed scalar diffusions.
  Bernoulli 19, no.1, 44-63.
• Pokern, Y., Stuart, A.M., van Zanten, J.H. (2013).
  Posterior consistency via precision operators for Bayesian drift estimation in SDEs.
  Stochastic Process. Appl. 123, no. 2, 603-628.

2012

• Belitser, E., Ghosal, S., van Zanten, J.H. (2012).
  Optimal two-stage procedures for estimating location and size of maximum of multivariate regression functions.
  Ann. Statist. 40, no. 6, 2850-2876.
• Roth, M., Buishand T.A., Jongbloed, G., Klein Tank, A.M.G., van Zanten, J.H. (2012).
  A regional peaks-over-threshold model in a nonstationary climate.
  Water Resour. Res. 48, W11533, 12 pp., doi:10.1029/2012WR012214.
• De Jonge, R., van Zanten, J.H. (2012).
  Adaptive estimation of multivariate functions using conditionally Gaussian tensor-product spline priors.
  Electron. J. Stat. 6, 1984-2001.

2011

• Knapik, B.T., van der Vaart, A.W., van Zanten, J.H. (2011).
  Bayesian inverse problems with Gaussian priors.
  Ann. Statist. 39, no. 5, 2626–2657.
• van Es, A.J., Spreij, P.J.C., van Zanten, J.H. (2011).
  Nonparametric methods for volatility density estimation.
  In: Advanced mathematical methods for finance, eds: Di Nunno, Oksendal, pp. 293–312, Springer, Heidelberg.
• van der Vaart, A.W., van Zanten, J.H. (2011).
  Information Rates of Nonparametric Gaussian Process Methods.
  J. Mach. Learn. Res. 12, 2095–2119.
• Gasbarra, D., Sottinen, T., van Zanten, J.H. (2011).
  Conditional full support of Gaussian processes with stationary increments.
  J. Appl. Probab. 48, no. 2, 561–568.

2010

• van Zanten, J.H. (2010).
  Comments on “PCA based Hurst exponent estimator for fBm signals under disturbances”.
  IEEE Trans. Signal Process. 58, no. 8, 4466–4467.
• de Jonge, R., van Zanten, J.H. (2010).
  Adaptive nonparametric Bayesian inference using location-scale mixture priors.
  Ann. Statist. 38, no. 6, 3300–3320.

2009

• van Zanten, J.H. (2009).
  On Brownian motion as a prior for nonparametric regression.
  Statist. Decisions 27, no. 4, 335–356.
• Panzar, L., van Zanten, J.H. (2009).
  Nonparametric Bayesian inference for ergodic diffusions.
  J. Statist. Plann. Inference 139, no. 12, 4193–4199.
• van der Vaart, A.W., van Zanten, J.H. (2009).
  Adaptive Bayesian estimation using a Gaussian random field with inverse Gamma bandwidth.
  Ann. Statist. 37, no. 5B, 2655–2675.
• Aurzada, F., Ibragimov, I.A., Lifshits, M.A., van Zanten, J.H (2009).
  Small deviations of smooth stationary Gaussian processes.
  Theory Probab. Appl. 53 (2009), no. 4, 697–707.

2008

• van der Vaart, A.W., van Zanten, J.H. (2008).
  Reproducing kernel Hilbert spaces of Gaussian priors.
  In: Pushing the limits of contemporary statistics: contributions in honor of Jayanta K. Ghosh, Inst. Math. Stat. Collect., 3, pp. 200–222, Beachwood, OH.
• van der Vaart, A.W., van Zanten, J.H. (2008).
  Rates of contraction of posterior distributions based on Gaussian process priors.
  Ann. Statist. 36, no. 3, 1435–1463.
• van Zanten, J.H., Zareba, P. (2008).
  A note on wavelet density deconvolution for weakly dependent data.
  Stat. Inference Stoch. Process. 11, no. 2, 207–219.
• van Zanten, J.H. (2008).
  A remark on the equivalence of Gaussian processes.
  Electron. Commun. Probab. 13, 54–59.

2007

• van der Vaart, A.W., van Zanten, J.H. (2007).
  Bayesian inference with rescaled Gaussian process priors.
  Electron. J. Stat. 1, 433–448.
• van Zanten, J.H. (2007).
  When is a linear combination of independent fBm’s equivalent to a single fBm?
  Stochastic Process. Appl. 117, no. 1, 57–70.

2006

• van der Meulen, F.H., van der Vaart, A.W., van Zanten, J.H. (2006).
  Convergence rates of posterior distributions for Brownian semimartingale models.
  Bernoulli 12, no. 5, 863–888.
• Dzhaparidze, K., van Zanten, J.H., Zareba, P. (2006).
  Representations of isotropic Gaussian random fields with homogeneous increments.
  J. Appl. Math. Stoch. Anal. 2006, Art. ID 72731, 25 pp.

2005

• Dzhaparidze, K., van Zanten, J.H., Zareba, P. (2005).
  Representations of fractional Brownian motion using vibrating strings.
  Stochastic Process. Appl. 115, no. 12, 1928–1953.
• van Zanten, J.H. (2005). On the rate of convergence of the maximum likelihood estimator in Brownian semimartingale models.
  Bernoulli 11, no. 4, 643–664.
• van der Vaart, A.W., van Zanten, J.H. (2005).
  Donsker theorems for diffusions: necessary and sufficient conditions.
  Ann. Probab. 33, no. 4, 1422–1451.
• Dzhaparidze, K., van Zanten, J.H. (2005).
  Optimality of an explicit series expansion of the fractional Brownian sheet.
  Statist. Probab. Lett. 71, no. 4, 295–301.
• Dzhaparidze, K., van Zanten, J.H. (2005).
  Krein’s spectral theory and the Paley-Wiener expansion for fractional Brownian motion.
  Ann. Probab. 33, no. 2, 620–644.
• van Es, A.J., Spreij, P., van Zanten, J.H. (2005). Nonparametric volatility density estimation for discrete time models. J. Nonparametr. Stat. 17, no. 2, 237–251.

2004

• Dzhaparidze, K. (2004), van Zanten, J.H. (2004).
  A series expansion of fractional Brownian motion.
  Probab. Theory Related Fields 130, no. 1, 39–55.

2003

• van Zanten, J.H. (2003). On empirical processes for ergodic diffusions and rates of convergence of M-estimators. Scand. J. Statist. 30, no. 3, 443–458.
• van Es, A.J., Spreij, P.J.C., van Zanten, J.H. (2003).
  Nonparametric volatility density estimation.
  Bernoulli 9, no. 3, 451–465.
• van Zanten, J.H. (2003).
  On uniform laws of large numbers for ergodic diffusions and consistency of estimators.
  Stat. Inference Stoch. Process. 6, no. 2, 199–213.

2002

• van Zanten, J.H. (2002). Continuous Ocone martingales as weak limits of rescaled martingales. Electron. Comm. Probab. 7, 215–222 (electronic). With erratum.

2001

• van Zanten, J.H. (2001). Rates of convergence and asymptotic normality of kernel estimators for ergodic diffusion processes. J. Nonparametr. Statist. 13, no. 6, 833–850.
• van Zanten, J.H. (2001). A note on consistent estimation of multivariate parameters in ergodic diffusion models. Scand. J. Statist. 28, no. 4, 617–623.
• Dzhaparidze, K., van Zanten, J.H. (2001).
  On Bernstein-type inequalities for martingales.
  Stochastic Process. Appl. 93, no. 1, 109–117.

2000

• van Zanten, J.H. (2000). On the uniform convergence of the empirical density of an ergodic diffusion. Stat. Inference Stoch. Process. 3, no. 3, 251–262.
• Dzhaparidze, K., Spreij, P.J C., van Zanten, J.H. (2000). Some aspects of modeling and statistical inference for financial models. Statist. Neerlandica 54, no. 3, 265–292.
• van Zanten, J.H. (2000).
  A multivariate central limit theorem for continuous local martingales.
  Statist. Probab. Lett. 50, no. 3, 229–235.