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Adaptive Bayes sum test for the equality of two nonparametric functions

机译：两个非参数函数是否相等的自适应贝叶斯和检验

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摘要

The statistical difference among massive data sets or signals is of interest to many diverse fields including neurophysiology, imaging, engineering, and other related fields. However, such data often have nonlinear curves, depending on spatial patterns, and have non-white noise that leads to difficulties in testing the significant differences between them. In this paper, we propose an adaptive Bayes sum test that can test the significance between two nonlinear curves by taking into account spatial dependence and by reducing the effect of non-white noise. Our approach is developed by adapting the Bayes sum test statistic by Hart. The spatial pattern is treated through Fourier transformation. Resampling techniques are employed to construct the empirical distribution of test statistic to reduce the effect of non-white noise. A simulation study suggests that our approach performs better than the alternative method, the adaptive Neyman test by Fan and Lin. The usefulness of our approach is demonstrated with an application in the identification of electronic chips as well as an application to test the change of pattern of precipitations.
机译：海量数据集或信号之间的统计差异引起许多不同领域的关注，包括神经生理学，影像学，工程学和其他相关领域。但是，此类数据通常具有非线性曲线（取决于空间模式），并且具有非白噪声，导致难以测试它们之间的显着差异。在本文中，我们提出了一种自适应贝叶斯和检验，该检验可以考虑空间依赖性并减少非白噪声的影响，从而测试两条非线性曲线之间的显着性。我们的方法是通过调整Hart的贝叶斯和检验统计量开发的。通过傅立叶变换处理空间模式。采用重采样技术来构建测试统计量的经验分布，以减少非白噪声的影响。仿真研究表明，我们的方法比Fan和Lin的自适应Neyman检验更好。我们的方法的有用性通过在电子芯片识别中的应用以及对降水模式变化的测试中得到了证明。

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