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The effects of error magnitude and bandwidth selection for deconvolution with unknown error distribution

机译:误差大小和带宽选择对未知误差分布的反卷积的影响

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摘要

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 these 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 by 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.
机译:在实际应用中的反卷积问题中,错误分布通常是未知的。因此,经常在这些研究中进行单独的独立实验以收集其他噪声数据。在本文中,我们研究了受污染的样本与附加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,并根据误差幅度研究了其渐近性质。然后,我们结合了Bootstrap方法和模拟外推的思想,提出了一种数据驱动的带宽选择算法。通过仿真研究评估了所提出方法的有限样本性能以及误差幅度的影响。进行了基因Illumina BeadArray研究的真实数据分析,以说明所提出方法的使用。

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