Nonparametric adaptive estimation for grouped data

Céline Duval; Johanna Kappus

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arXiv · 1606.01117

Nonparametric adaptive estimation for grouped data

Céline Duval·Johanna Kappus

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Abstract

The aim of this paper is to estimate the density f of a random variable X when one has access to independent observations of the sum of K $\ge$ 2 independent copies of X. We provide a constructive estimator based on a suitable definition of the logarithm of the empirical characteristic function.We propose a new strategy for the data driven choice of the cut-off parameter. The adaptive estimator is proven to be minimax-optimal up to some logarithmic loss. A numerical study illustrates the performances of the method. Moreover, we discuss the fact that the definition of the estimator applies in a wider context than the one considered here.

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Céline Duval, Johanna Kappus. 2016-06-03. Nonparametric adaptive estimation for grouped data. https://arxiv.org/abs/1606.01117

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