Academic Report of School of Mathematical Sciences [2026] No. 082

(Series Report for High-Level University Construction No. 1341)

Title：MULTIPLIER BOOTSTRAP MEETS HIGH-DIMENSIONAL PCA: THE GOOD, THE BAD AND THE MODIFICATION

Speaker：Professor Wang Zhou (National University of Singapore)

Time：10:30-11:30, Aug. 6, 2026

Location：Conference Room 1425, Huiwen Building

Abstract: In this paper, we examine the feasibility (i.e., both the good advantages and the bad limitations) and the adaptivity (i.e., the potential for beneficial modifications) of employing multiplier bootstrap to analyze the asymptotic

distributions of the largest eigenvalues of potentially spiked high-dimensional sample covariance matrices. Our findings and proposed algorithms demonstrate that multiplier bootstrap remains valid, provided the multipliers are appropriately chosen and the bootstrap procedures are applied multiple times with suitable corrections.

Speaker Profile：Zhou Wang has been a faculty member in the Department of Statistics at the National University of Singapore since July 2004 and was appointed tenured professor in January 2009. He is currently a professor at the National University of Singapore. His primary research interests include random matrices, SLE, and high-dimensional statistics. In recent years, he has published more than 90 high-quality academic papers. Among these, more than 20 have appeared in internationally recognized top-tier journals in probability and statistics, including Annals of Statistics, Journal of the American Statistical Association, Biometrika, Annals of Probability, Probability Theory and Related Fields, and Annals of Applied Probability. In 2012, he was elected a Member of the International Statistical Institute. In 2012, he received the “Outstanding Scientist Award” from the National University of Singapore. In 2021, he was elected a Fellow of the International Statistical Institute. Since 2005, he has led more than ten research projects funded by the Singapore government.

Faculty and students are welcome to attend!

Invited by: Yan Zhou

School of Mathematical Sciences

August 3, 2026