Abstract
Abstract In this paper we consider a random variable Y contaminated by an additive noise Z from a known distribution. Our purpose is to test the distribution of the unobserved random variable Y. We propose a data driven statistic based on a nonparametric expansion of the density of Y + Z, which can be applied as well in the continuous case as in the discrete case. The problem is considered at first in the univariate case, and then extended in a multivariate setting with a bootstrap procedure. Finite-sample properties are examined through Monte Carlo and Quasi Monte Carlo simulations in univariate and bivariate cases.
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