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Alexander MEISTER (Université de Rostock) – “Nonparametric density estimation for intentionally corrupted functional data”
September 10, 2:00 pm - 3:15 pm
The Statistical Seminar: Every Monday at 2:00 pm.
Time: 2:00 pm – 3:15 pm
Date: 10th of September 2018
Place: Room 3001.
Alexander MEISTER (Université de Rostock) – “Nonparametric density estimation for intentionally corrupted functional data“
Abstract: We consider statistical models where functional data are artificially contaminated by independent Wiener processes in order to satisfy privacy constraints. We show that the corrupted observations have a Wiener density which determines the distribution of the original functional random variables uniquely, and we construct a nonparametric estimator of that density. We derive an upper bound for its mean integrated squared error which has a polynomial convergence rate, and we establish an asymptotic lower bound on the minimax convergence rates which is close to the rate attained by our estimator. Our estimator requires the choice of a basis and of two smoothing parameters. We propose data-driven ways of choosing them and prove that the asymptotic quality of our estimator is not significantly affected by the empirical parameter selection. We examine the numerical performance of our method via simulated examples.
Cristina BUTUCEA, Alexandre TSYBAKOV, Julie JOSSE, Eric MOULINES, Mathieu ROSENBAUM