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.

中文翻译：

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误差幅度和带宽选择对误差分布未知的反卷积的影响

在实际应用的反卷积问题中，误差分布通常是未知的。因此，经常进行单独的独立实验来收集这些研究中的额外噪声数据。在本文中，我们研究了来自受污染样本和附加噪声样本的非参数反卷积估计。提出了一种基于脊的核反卷积估计器，并根据误差幅度研究了其渐近特性。然后，我们通过结合自举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。通过模拟研究评估了所提出方法的有限样本性能和误差幅度的影响。