Institute for Mathematical Sciences Programs & Activities
Self-normalized Asymptotic Theory in Probability, Statistics and Econometrics
(1 - 30 May 2014)
- Ngai Hang Chan (The Chinese University of Hong Kong)
- Xiaohong Chen (Yale University)
- Qi-Man Shao (The Chinese University of Hong Kong)
- Louis Chen (National University of Singapore)
- Guangming Pan (Nanyang Technological University)
- Yeneng Sun (National University of Singapore)
- Wang Zhou (National University of Singapore)
Asymptotic theory has played a fundamental role in probability and statistics. The law of large numbers, the central limit theorem, the Edgeworth expansion, the Cramer moderate deviation and the Varadhan large deviation are cores of the asymptotic theory. The classical limit theorems for sums of independent random variables are well-established with necessary and sufficient moment conditions. Driven by the applications in statistics, econometrics, physics, bioinformatics and other subjects, extensions to dependent variables and high dimensional data have been actively studied and various new methods are also developed. Noticeable new methods and new developments include:
- Stein's method for normal and non-normal approximation which works not only for independent random variables but also for dependent variables and can also give bounds for accuracy of approximations,
- Self-normalized limit theorems which require no moment assumptions or much less moment assumptions than the classical limit theorems need,
- Random matrix theory.
Recent books "Self-normalized processes: theory and statistical applications" (2009) by de la Pena, Lai and Shao, "Normal approximation by Stein's method" (2011) by Chen, Goldstein and Shao, "Spectral analysis of large dimensional random matrices" (2010) by Bai and Silverstein, "Statistics for High-Dimensional Data: Methods, Theory and Applications" (2011) by Buhlmann and van de Geer are important contributions to the asymptotic theory and all testify the vitality of the field.
Besides its long history and recent advances, asymptotic theory is a key ingredient for a variety of applications, especially in statistical inference, econometrics and bioinformatics. For example, Cramer type moderate deviations quantify the accuracy of estimated p-values which are crucial in the study of multiple hypothesis tests.
This program will provide the probabilists, statisticians and econometricians a unique platform to discuss interesting fundamental problems and results and explore possible solutions related to asymptotic theory. It is also intended to bring young researchers to the frontier of this fascinating area.
- Research and Informal Discussions: 5 - 9 May 2014 & 26 - 30 May 2014
- Tutorial on Introduction to Self-normalized Limit Theory: 14 - 16 May 2014
- Tutorial on Introductory Econometrics: 14 - 16 May 2014
- Workshop on Self-normalized Asymptotic Theory in Probability, Statistics and Econometrics: 19 - 23 May 2014
* Our office will be closed on the following dates being Singapore public holidays.
1 May 2014 - Labour Day
13 May 2014 - Vesak Day
Students and researchers who are interested in attending these activities are requested to complete the online registration form.
The following do not need to register:
- Those invited to participate.
- Those applying for financial support.