Nonparametric density estimation for intentionally corrupted functional data
| Autor: | Aurore Delaigle, Alexander Meister |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Polynomial 62G07 62M99 62H30 Estimator Statistical model Mathematics - Statistics Theory Statistics Theory (math.ST) Minimax Upper and lower bounds Rate of convergence FOS: Mathematics Applied mathematics Statistics Probability and Uncertainty Random variable Smoothing Mathematics |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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