Prof. Jianfeng Yao 姚建峰 教授
University of California, Irvine
This talk presents deviation tests for high-dimensional mean vectors based on control feedback and two-armed bandit processes.The method extends to two-sample problems and achieves good finite-sample performance. It lies in random matrix theory and high-dimensional statistics, where Professor Yao is a leading scholar.
Abstract 摘要
This paper investigates testing for deviation of a high-dimensional mean vector. In contrast to the standard one-sample significance test of the form: H₀: μ = μ₀ versus H₁: μ ≠ μ₀, we focus on testing the deviation: H₀: ||μ − μ₀||₂ ≥ d₀ versus H₁: ||μ − μ₀||₂ < d₀ for a prespecified length d₀> 0. Constructing a valid test statistic for this problem is technically nontrivial. By applying the concept of positive and negative feedback processes from control theory, we propose a test statistic based on a two-armed bandit (TAB) process. These deviation tests are also extended to the two-sample setting. Simulation experiments confirm good performance of the tests in finite samples. Finally, a real data analysis demonstrates the practical significance of the proposed deviation tests.
Speaker Biography 讲者简介
Professor Yao is an international leading scholar in random matrix theory and high-dimensional statistics. His book Large Sample Covariance Matrices and High-Dimensional Data Analysis (Cambridge University Press, 2015, co-authored with Zhidong Bai and Shurong Zheng) is an authoritative reference of the field. Professor Yao received a few awards for his research contributions. He was elected as a Fellow of the Institute of Mathematical Statistics (U.S.A.) with the citation: "For influential contribution to the inferential aspects of random matrix theory in the analysis of high-dimensional data". Professor Yao is currently the Scientific Secretary and a member of the Executive Committee of the Bernoulli Society for Mathematical Statistics and Probability. He has been on the editorial board of several leading journals including Bernoulli, Journal of Multivariate Analysis and Random Matrices: Theory and Applications.
Topics 涉及主题
Deviation Tests for High-Dimensional Mean Vectors Two-Armed Bandit-Based Test Construction Random Matrix Theory and High-Dimensional Statistics