Adaptive quantile estimation in deconvolution with unknown error distribution. (English) Zbl 1388.62095

Dattner, Itai; Reiß, Markus; Trabs, Mathias

Bernoulli 22, No. 1, 143-192 (2016).

Summary: Quantile estimation in deconvolution problems is studied comprehensively. In particular, the more realistic setup of unknown error distributions is covered. Our plug-in method is based on a deconvolution density estimator and is minimax optimal under minimal and natural conditions. This closes an important gap in the literature. Optimal adaptive estimation is obtained by a data-driven bandwidth choice. As a side result, we obtain optimal rates for the plug-in estimation of distribution functions with unknown error distributions. The method is applied to a real data example.

MSC:

62G07	Density estimation
62G20	Asymptotic properties of nonparametric inference

Keywords:

adaptive estimation; deconvolution; distribution function; minimax convergence rates; plug-in estimator; quantile function; random Fourier multiplier

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