Journal article

Nonparametric density estimation for intentionally corrupted functional data

A Delaigle, A Meister

Statistica Sinica | Academia Sinica, Institute of Statistical Science | Published : 2020

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, masked near the origin, 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 parameter..

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