A1046
Title: Simultaneous bootstrap inference for high-dimensional spatial median with applications
Authors: Liuhua Peng - The University of Melbourne (Australia) [presenting]
Guanghui Cheng - Guangzhou University (China)
Abstract: This paper studies Gaussian and bootstrap approximation of the maximum of the sample spatial median under elliptical symmetric distribution with applications in simultaneous inference for the population spatial median. Based on a novel Bahadur representation of the sample spatial median with a maximum-norm bound on the remainder term, we establish Gaussian approximation of the maximum of sample spatial median under Kolmogorov distance. We further propose the multiplier bootstrap to approximate the distribution of the maximum of sample spatial median and justify its consistency. Our theoretical results allow the exponential divergence rate of the dimension as in the ``ultra-high'' dimensional region. Moreover, applications of the bootstrap approximation on simultaneous inference for the spatial median have been investigated. The finite-sample performance via Monte Carlo simulations supports the proposed methods.
