DeepAI
Log In Sign Up

Nonparametric density estimation for intentionally corrupted functional data

12/17/2019
by   Aurore Delaigle, et al.
0

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 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.

READ FULL TEXT

page 1

page 2

page 3

page 4

03/01/2022

Adaptive nonparametric estimation in the functional linear model with functional output

In this paper, we consider a functional linear regression model, where b...
07/31/2019

Kernel Density Estimation for Undirected Dyadic Data

We study nonparametric estimation of density functions for undirected dy...
06/17/2021

Minimax Estimation of Partially-Observed Vector AutoRegressions

To understand the behavior of large dynamical systems like transportatio...
01/28/2021

Adaptive Estimation of Quadratic Functionals in Nonparametric Instrumental Variable Models

This paper considers adaptive estimation of quadratic functionals in the...
10/07/2012

Privacy Aware Learning

We study statistical risk minimization problems under a privacy model in...