Rastogi, Abhishake2024-07-122024-07-122019Rastogi, A. (2019). Regularization schemes for statistical inverse problems. International Conference of Mathematical Sciences (ICMS 2019). s. 185.978-605-2124-29-1https://hdl.handle.net/20.500.12415/2163We study a statistical inverse learning problem, where we observe the noisy image of a quantity through a operator at some random design points. We consider the regularization schemes to reconstruct the estimator of the quantity for the ill-posed inverse problem. We develop a theoretical analysis for the minimizer of the regularization scheme using the ansatz of reproducing kernel Hilbert spaces. We discuss optimal rates of convergence for the proposed scheme, uniformly over classes of admissible solutions, defined through appropriate source conditions.enCC0 1.0 Universalinfo:eu-repo/semantics/openAccessStatistical inverse problemTikhonov regularizationReproducing kernel Hilbert spaceGeneral source conditionMinimax convergence ratesArticle186185