Supersmooth functional data analysis and PCA-preprocessing

• Applicant: Professor Dr. Alexander Meister
• Subject Area: Mathematics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 460867398

We consider nonparametric regression models with infinite-dimensional covariates (functional data) and related models with high-dimensional covariates. Building upon the obtained asymptotic results for local polynomial estimators for functional data, we intend to improve the convergence rates by imposing specific constraints on the functional covariates and by "sparsification" to control anti-concentration bounds for random polynomials. We investigate information-theoretic aspects of the derived rates, and address adaptivity by data-driven parameter selection. Moreover, we consider functional regression for partially observed covariates, asymptotic equivalence in high-dimensional additive models, and continue investigating specific aspects of time-series prediction with the aim of generalizing previously obtained sharp oracle inequalities to nonlinear setups.

• DFG Programme: Research Units
• Subproject of: FOR 5381: Mathematical Statistics in the Information Age - Statistical Efficiency and Computational Tractability
• International Connection: Austria
• Partner Organisation: Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
• Cooperation Partner: Professor Dr. Moritz Jirak