Adaptive quantile estimation in deconvolution with unknown error distribution

被引：18
|
作者：
Dattner, Itai [1 ]
Reiss, Markus [2 ]
Trabs, Mathias [2 ]
机构：
[1] Univ Haifa, Dept Stat, IL-3498838 Haifa, Israel
[2] Humboldt Univ, Inst Math, D-10099 Berlin, Germany
来源：
BERNOULLI | 2016年 / 22卷 / 01期
关键词：
adaptive estimation; deconvolution; distribution function; minimax convergence rates; plug-in estimator; quantile function; random Fourier multiplier; NONPARAMETRIC-ESTIMATION; DENSITY-ESTIMATION; LEVY PROCESSES; OPTIMAL RATES; CONVERGENCE; THEOREM;
D O I：
10.3150/14-BEJ626
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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.
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页码：143 / 192
页数：50
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