A0151
Title: Gaussian approximation for thresholding statistics
Authors: Yumou Qiu - Peking University (China) [presenting]
Abstract: Thresholding statistics that sum the thresholded standardized statistics over many components are more powerful than the sum-of-square type and maximum type test statistics in detecting sparse and weak signals for global hypotheses. However, the asymptotic distribution of the thresholding statistics has only been derived under the assumption of independent variables or certain conditions on the mixing dependence among variables. Gaussian approximation result is established for the thresholding statistics under general covariance structures and high-dimensionality. Due to the non-smoothness of the thresholding function, existing techniques to show Gaussian approximation results for the sum-of-square and maximum statistics can not be applied. A novel method has been developed to establish the Gaussian approximation results for thresholding statistics. Based on this result, a bootstrap procedure is constructed to approximate the distribution of the thresholding statistics under a high-dimensional setting. Simulation studies are conducted to show the utility of the proposed approach.
