Wild Bootstrap Tests

In this article, we have derived tests based on the wild bootstrap that allow checking for differences between two irregular signals observed with additive noise where the latter consists of independent but not necessarily identically distributed random variables. The signals are first denoised by kernel estimates and then compared by looking at the integrated squared difference. The bound between accepting and rejecting the hypothesis of equal signals are determined by the wild bootstrap and numerically calculated by Monte Carlo simulation. The test is applied to all pairwise rows and columns of two images, which results in an algorithm that allows detection of defects and additional information on their location and shape surface inspection problems. The idea and theory of the test may be straightforwardly extended to the direct comparison of two images. This is computationally less expensive than doing all the row- and columnwise tests, but it provides less information.