Abstract:
Gaussian approximation means that a function of independent random variables can be approximated by the function of independent normally distributed random variables. This is a powerful tool in limit theory in probability and large sample theory in statistics. Berry–Esseen type bounds for Gaussian approximation of standardized sums have been extensively studied under finite moment conditions for lower dimensional data and under sub-exponential moment conditions for high dimensional data. However, since the standardized coefficients such as the population standard deviations are typically unknown, it is essential for statistical inference to study the Gaussian approximation of self-normalized sums. In this talk, we shall give a brief review on self-normalized limit theory and establish a Cramér type moderate deviation theorem for self-normalized high dimensional Gaussian approximation under finite moment conditions.
Biography:
Dr. Qi-Man Shao is the Founding Chairman of the Department of Statistics and Data Science and Chair Professor at the Southern University of Science and Technology. He earned a bachelor's degree in Mathematics in 1983 and a master's degree in Statistics & Probability in 1986 from Hangzhou University (now known as Zhejiang University). Then he received a Ph.D. degree in Statistics & Probability from the University of Science and Technology of China in 1989. He was a faculty member at Hangzhou University, National University of Singapore, University of Oregon, the Hong Kong University of Science and Technology and the Chinese University of Hong Kong respectively. Dr. Shao has made significant contributions to the limit theory in probability and statistics. In particular, he has systematically developed the self-normalized limit theory and established the self-normalized large and moderate deviation theorems. In 2015, Dr. Shao was awarded the State Natural Science Award (2nd class). He was an invited speaker at the International Congress of Mathematicians in 2010 and an elected Fellow of the Institute of Mathematical Statistics (IMS) in 2001. Dr. Shao has made important contributions to professional service. He was an Associate Editor of the Annals of Statistics and Bernouli and currently is a council member of IMS and a co-Editor of the Annals of Applied Probability.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.