Compatibility test between the simulated and real test data under small samples conditions
Tang Xujin, Lei Wang, Zhang Shike, Zhang Linke章林柯 · 2014
Data simulation shows an increasing importance under small samples conditions due to the difficulties of obtaining real data in acoustic fault identification. Compatibility test between the simulated and real data in small samples size is a key requirement for guaranteeing the validity of the simulated data. Most existing methods for compatibility test, such as Kolmogorov-Smirnov test, have a large requirement on test data amounts. One representative method for univariate data in small samples sizes is Wilcoxon rank sum test, but it is only suitable for detecting distributions differences from mean changes. In this paper, we address a novel compatibility test method under small samples conditions. Herein the maximum mean discrepancy (MMD), which is introduced for measuring the difference of the probability distributions between the simulated and real samples, is considered as the test statistic, and a Gaussian kernel in a reproducing kernel Hilbert space (RKHS) is adopted to construct such test statistic. So the resulting compatibility test problem is formulated in the terms of computing the MMD based on RKHS. Experimental results demonstrate that the proposed approach can achieve a better performance for distinguishing the distribution differences under small samples situations than traditional test methods.