题目：Another look at Bandwidth-free Inference, a sample splitting approach

主讲人：伊利诺伊大学香槟分校 邵晓峰教授

主持人：统计学院 常晋源教授

时间：2024年1月13日（周六）上午9:30-11:00

地点：腾讯会议，461-464-147

报告摘要：

The bandwidth-free tests for a multi-dimensional parameter have attracted considerable attention in econometrics and statistics literature. These tests can be conveniently implemented due to their tuning-parameter free nature and possess more accurate size as compared to the traditional heteroskedasticity and autocorrelation consistent-based approaches. However, when sample size is small/medium, these bandwidth-free tests exhibit large size distortion when both the dimension of the parameter and the magnitude of temporal dependence are moderate, making them unreliable to use in practice. In this talk, we propose a sample splitting-based approach to reduce the dimension of the parameter to one for the subsequent bandwidth-free inference. Our SS–SN (sample splitting plus self-normalisation) idea is broadly applicable to many testing problems for time series, including mean testing, testing for zero autocorrelation, and testing for a change point in multivariate mean, among others. Specifically, we propose two types of SS–SN test statistics and derive their limiting distributions under both the null and alternatives and show their effectiveness in alleviating size distortion via simulations. In addition, we obtain the limiting distributions for both SS–SN test statistics in the multivariate mean testing problem when the dimension is allowed to diverge.

主讲人简介：

Dr. Shao is Professor of Statistics and PhD program director, at the Department of Statistics, University of Illinois at Urbana-Champaign (UIUC). He received his PhD in Statistics from University of Chicago in 2006 and has been on the UIUC faculty since then. Dr. Shao's research interests include time series analysis, high-dimensional data analysis, functional data analysis, change-point analysis, resampling methods and asymptotic theory. He is an elected ASA and IMS fellow.