B1671
Title: New resampling schemes for composite goodness-of-fit tests with kernels
Authors: Nicolas Rivera - Universidad de Valparaiso (Chile) [presenting]
Tamara Fernandez - Universidad Adolfo Ibanez (Chile)
Wenkai Xu - University of Tuebingen (Germany)
Abstract: A new resampling scheme is studied for Kernel tests in the setting of composite goodness-of-fit problems in order to determine rejection regions. Traditionally, kernel tests have favoured the wild bootstrap resampling scheme because of its efficiency as it avoids the need to recompute the kernel test statistic in each iteration, unlike other alternatives like the parametric bootstrap. However, in the setting of composite goodness-of-fit testing, it can be empirically observed that the Wild bootstrap fails to provide good rejection regions, leading to a significant loss of statistical power. Therefore, less efficient resampling schemes have to be used instead. To address this issue, it is proposed to fix the wild bootstrap procedure by adding a correction term that is computed by using one sample of the parametric bootstrap, to then perform the usual wild bootstrap procedure. The key advantage of the approach is that it requires just one iteration of the parametric bootstrap, making it nearly as cost-effective as the traditional wild bootstrap, yet significantly more powerful. Theoretical results are provided, showing the correctness of the approach, as well as experimental results demonstrating that the methodology indeed results in more powerful tests.
