Resampling and model validation for spatio-temporal data
A03 employs complexity-reducing structural assumptions to construct resampling-based inference procedures and develops statistical tools to quantify deviations from such assumptions. A particular focus is on methods that allow to differentiate practically relevant and non-relevant deviations from simplifying assumptions such as, e.g., separability or low-rank approximations. In the long term, this project investigates resampling and model validation for multi-resolution approximations, high-dimensional modeling, and statistical inference for complex non-stationary spatio-temporal data.
Project Leaders
Prof. Dr. Holger Dette
Faculty of Mathematics - Chair of Stochastics
Ruhr University Bochum
Prof. Dr. Carsten Jentsch
Department of Statistics - Chair of Business and Social Statistics
TU Dortmund University
Summary
In spatio-temporal data analysis structural assumptions on the covariance function, such as symmetry, (spatial) isotropy or various forms of separability are often imposed to improve estimation efficiency and to achieve computational benefits, such as reduced computation time and lower data storage requirements. They are rarely made because one believes these to hold exactly, but with the hope that the deviations from the postulated model are relatively small, such that the application of more efficient statistical inferential procedures tailored for the structural assumptions is possible. Therefore, in practice, one is generally confronted with the tradeoff of balancing a potentially larger bias because of overly restrictive model assumptions against a potentially smaller variance due to the additional structure imposed.
In this project, we make use of complexity-reducing structural model assumptions to develop new and more efficient resampling-based inference procedures for the analysis of spatio-temporal data. We will develop statistical methods to quantify deviations from such assumptions and construct suitable tests for model validation. In addition to methodology for exact hypotheses (e.g. exact separability of the covariance), we will also supply methodology that allows to quantify deviations and to differentiate between practically relevant and non-relevant deviations from the postulated model assumptions. In particular, we investigate the statistical properties of these methods, such as validity or consistency, from an asymptotic point of view considering different sampling schemes in space and time.
Besides commonly used structural assumptions imposed on the covariance function such as parametric models, symmetry, (spatial) isotropy, or various forms of separability, our focus is also on complexity-reducing approaches including sparsity, low rank methods, separable expansions for covariance estimation and also nonlinear methods.
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Aue, A., Kühnert, S., Rice, G., VanderDoes, J. (2026). An operator-level ARCH model. arXiv. DOI: 10.48550/arXiv.2603.10272.
Bai, L., Dette, H. (2025). Measuring deviations from spherical symmetry. arXiv. DOI: 10.48550/arXiv.2510.18598.
Bai, L., Dette, H., Wu, W. (2025). A Portmanteau test for multivariate non-stationary functional time series with an increasing number of lags. arXiv. DOI: 10.48550/arXiv.2501.00118.
Bai, L., Dette, H., Yuan, Z. (2026). Validating spatial-temporal separability for stationary processes. arXiv. DOI: 10.48550/arXiv.2603.26369.
Bai, L., Hu, Q., Wu, W. (2026). Inference for structural changes in nonstationary functional time series with partial measurement error. To appear in Journal of the Royal Statistical Society Series B: Statistical Methodology.
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Bai, L., Wu, W. (2025). Uniform variance reduced simultaneous inference of time-varying correlation networks. IEEE Transactions on Information Theory 71 (12), 9647–9673. DOI: 10.1109/TIT.2025.3613143.
Bastian, P. (2025). Choosing the right norm for change point detection in functional data. Electronic Journal of Statistics 19 (2), 4637–4672. DOI: 10.1214/25-EJS2451.
Bastian, P. (2025). Detecting relevant deviations from the white noise assumption for non-stationary time series. Journal of Time Series Analysis. DOI: 10.1111/jtsa.70005.
Bastian, P., Basu, R., Dette, H. (2025). Uniform confidence bands for joint angles across different fatigue phases. New Trends in Functional Statistics and Related Fields, 33–42. DOI: 10.1007/978-3-031-92383-8_5.
Bastian, P., Bissantz, N. (2025). Detecting relevant dependencies under measurement error with applications to the analysis of planetary system evolution. arXiv. DOI: 10.48550/arXiv.2504.05055.
Bastian, P., Dette, H. (2026). Multiscale detection of practically significant changes in a gradually varying time series. Electronic Journal of Statistics 20 (1), 138–162. DOI: 10.1214/26-EJS2485.
Bastian, P., Dette, H., Dunsche, M. (2025). Differentially private testing for relevant dependencies in high dimensions. arXiv. DOI: 10.48550/arXiv.2511.17167.
Bastian, P., Kutta, T., Basu, R., Dette, H. (2025). Monitoring time series for relevant changes. arXiv. DOI: 10.48550/arXiv.2509.01756.
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Faymonville, M. , Jentsch, C. (2025). Joint semi-parametric INAR bootstrap inference for model coefficients and innovation distribution. arXiv. DOI: 10.48550/arXiv.2507.11124.
Faymonville, M., Jentsch, C., Paparoditis, E. (2025). Predictive inference for discrete-valued time series. arXiv. DOI: 10.48550/arXiv.2507.16035.
Faymonville, M., Jentsch, C., Weiß, C.H. (2025). Semi-parametric goodness-of-fit testing for INAR models. Bernoulli 31 (4), 3213-3234. DOI: 10.3150/24-BEJ1844.
Flossdorf, J., Meyer, A., Artjuch, D., Schneider, J., Jentsch, C. (2025). Unsupervised movement detection in indoor positioning systems of production halls. TRR 391 Working Paper #9. DOI: 10.17877/DE290R-25841.
Heinrichs, F., Bastian, P., Dette, H. (2025). Sequential outlier detection in non-stationary time series. Journal of Time Series Analysis. DOI: 10.1111/jtsa.70043.
Kühnert, S., Park, J. (2025). Functional periodic ARMA processes. arXiv. DOI: 10.48550/arXiv.2507.18962.
Kühnert, S., Rice, G. and Aue, A. (2026). Estimating invertible processes in Hilbert spaces, with applications to functional ARMA processes. Bernoulli 32 (2), 1523–1546. DOI: 10.3150/25-BEJ1918.
Kutta, T., Dette, H., Wang, S. (2025). Multiscale change point detection for functional time series. arXiv. DOI: 10.48550/arXiv.2511.06870.
Kutta, T., Schumann, M., Dette, H. (2025). Inference for forecasting accuracy: pooled versus individual estimators in high-dimensional panel data. arXiv. DOI: 10.48550/arXiv.2512.15592.
Li, B., Qiao, X., Wu, W., Dette, H. (2025). Convergence of covariance and spectral density estimates for high-dimensional functional time series. arXiv. DOI: 10.48550/arXiv.2512.13310.
Ng, W. L., Tang, X., Cheung, M. L., Gao, J., Yau, C. Y., Dette, H. (2026). Inference for multiple change-points in piecewise locally stationary time series. arXiv. DOI: 10.48550/arXiv.2601.07400.
Quanz, P., Dette, H. (2025). Practically significant change points in high dimension - measuring signal strength pro active component. arXiv. DOI: 10.48550/arXiv.2508.21520.
Yuan, Z., Dette, H. (2025). Exponential inequalities for some mixing processes and dynamic systems. arXiv. DOI: 10.48550/arXiv.2208.11481.
Yuan, Z., Spindler, M. (2025). Bernstein-type inequalities and nonparametric estimation under near-epoch dependence. Journal of Econometrics 251, 106054. DOI: 10.1016/j.jeconom.2025.106054.