Wang Xiao-Feng, Ye Deping
Department of Quantitative Health Sciences/Biostatistics Section, Cleveland Clinic Foundation, Cleveland, OH 44195, USA.
J Nonparametr Stat. 2012 Jan 1;24(1):153-167. doi: 10.1080/10485252.2011.647024. Epub 2012 Jan 30.
The error distribution is generally unknown in deconvolution problems with real applications. A separate independent experiment is thus often conducted to collect the additional noise data in those studies. In this paper, we study the nonparametric deconvolution estimation from a contaminated sample coupled with an additional noise sample. A ridge-based kernel deconvolution estimator is proposed and its asymptotic properties are investigated depending on the error magnitude. We then present a data-driven bandwidth selection algorithm with combining the bootstrap method and the idea of simulation extrapolation. The finite sample performance of the proposed methods and the effects of error magnitude are evaluated through simulation studies. A real data analysis for a gene Illumina BeadArray study is performed to illustrate the use of the proposed methods.
在实际应用的反卷积问题中，误差分布通常是未知的。因此，在这些研究中经常进行单独的独立实验来收集额外的噪声数据。在本文中，我们研究了来自受污染样本并结合额外噪声样本的非参数反卷积估计。提出了一种基于岭的核反卷积估计器，并根据误差大小研究了其渐近性质。然后，我们提出了一种结合自助法和模拟外推思想的数据驱动带宽选择算法。通过模拟研究评估了所提方法的有限样本性能以及误差大小的影响。对基因Illumina BeadArray研究进行了实际数据分析，以说明所提方法的应用。
