Bio
Dr. Song Xi Chen is a University Chair Professor at School of Mathematical Sciences, Guanghua School of Management and Center for Statistical Science of Peking University, Peking, China. He received his B.Sc. and M.Sc. in Mathematics from Beijing Normal University in 1983 and 1988, respectively, and his Ph.D. in Statistics from Australian National University in 1993. His primary research interests include inference for high-dimensional data, environmental modeling, empirical likelihood, econometric theory and financial econometrics. He became a member of Chinese Academy of Sciences in 2021 and was elected as Fellow of the American Statistical Association and Fellow of the Institute of Mathematical Statistics (IMS) in 2009. He is also an Elected Member of International Statistical Institute, an Elected Council Member of IMS during 2016 – 2019 and an Elected Board Member of the International Chinese Statistical Association (ICSA) during 2008 – 2013. He is currently serving as Scientific Secretary of Bernoulli Society since 2019 and was selected to give Peter Hall Lecture at the 12th ICSA International Conference.
Abstract
Multi-level Thresholding for Detecting Rare and Faint Signals
The work considered in this talk was largely motivated by Professor Hall works on testing for high dimensional means. I will summarize latest research on detection of rare and faint signals in the mean and the covariance matrices, the two basic summary measures of distributions, by formulating multi-level thresholding tests (MTT). The detection boundary and the minimax properties of the MTTs are presented. The MTTs are shown to be powerful in detecting sparse and weak signals in thigh dimensional mean and covariances, leading to attractive detection boundary and attain the optimal minimax rate in the signal strength under different regimes of high dimensionality and the sparsity of the signals.