Adaptive Bayes sum test for the equality of two nonparametric functions

Abstract

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]. 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]. 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.

Keywords:

• Bayes sum test
• discrete Fourier transform
• Neyman test
• Laplace approximation
• resampling

Acknowledgements

This study was supported by a grant from the National Science Foundation (NSF-CNS 0964680) and National Science Foundation (NSF-CNS 1115839).