Abstract

We consider the problem of density estimation using noisy data containing small measurement errors. The only assumption on these errors is that the maximal measurement error is bounded by some real number converging to zero for sample size tending to infinity. We estimate the density by a standard kernel density estimate applied to the noisy data and propose data-dependent method for choosing its bandwidth. We derive an adaptation result for this estimate and analyze the expected L1 error of our density estimate depending on the smoothness of the density and the size of the maximal measurement error.

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