Adaptive quantile estimation in deconvolution with unknown error distribution

作者：Dattner Itai^*; Reiss Markus; Trabs Mathias

来源：Bernoulli, 2016, 22(1): 143-192.

DOI：10.3150/14-BEJ626

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

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.

• 出版日期2016-2