Wild bootstrap tests

The bootstrap method can be tested by means of detecting defects in various applications. The test involves the detection of differences between two noisy signals or images, which also works for noise with variable variance. Specifically, the test is the integrated squared difference between the signals after denoising them by local smoothing. In approximating the distribution of statistics of interest bootstraps are generally the tool. One useful test for bootstrap includes the defect detection in woven textures. The detection will first involve smoothing the surface under consideration locally and then compare the resulting denoised image with another one derived from a similar specimen or from a different part of the same specimen. The test works by detecting irregular signals in defects. By means of kernel estimates the signals are denoised and then compared by looking at the integrated squared difference. The defect areas are identified by scrutinizing rows and columns as well as diagonal cuts through the images.