Adaptive Bayes sum test for the equality of two nonparametric functions

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 [13 J.D. Hart, Frequentist-Bayes lack-of-fit tests based on Laplace approximations, J. Stat. Theory Practice 3 (2009), pp. 681–704. doi: 10.1080/15598608.2009.10411954[Taylor &; Francis Online] , [Google Scholar]]. 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 [9 J. Fan and S. Lin, Test of significance when data are curves, J. Amer. Math. Soc. 93 (1997), pp. 1007–1021.[Web of Science ®] , [Google Scholar]]. 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.