ON DECONVOLUTION OF DISTRIBUTION FUNCTIONS
ON DECONVOLUTION OF DISTRIBUTION FUNCTIONS
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DOI：
10.1214/11-aos907
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发表时间：
2011-10-01
影响因子：
4.5
通讯作者：
Juditsky, A.
中科院分区：
文献类型：
--
作者：
Dattner, I.;Goldenshluger, A.;Juditsky, A.
本文的主题是从有测量误差的观测值中估计连续分布函数的非参数估计问题。当未知分布的密度属于Sobolev类，且误差密度为一般光滑时，我们研究了该问题的极小极大复杂性。我们发展了基于经验特征函数直接逆的速率最优估计器。我们还得到了分布函数的极小极大仿射估计，它是由一个显式凸优化问题给出的。提出了这些估计器的自适应形式，并给出了一些数值结果，证明了所发展的方法具有良好的实际行为。
The subject of this paper is the problem of nonparametric estimation of a continuous distribution function from observations with measurement errors. We study minimax complexity of this problem when unknown distribution has a density belonging to the Sobolev class, and the error density is ordinary smooth. We develop rate optimal estimators based on direct inversion of empirical characteristic function. We also derive minimax affine estimators of the distribution function which are given by an explicit convex optimization problem. Adaptive versions of these estimators are proposed, and some numerical results demonstrating good practical behavior of the developed procedures are presented.