- 15:00-15:50 Some Testing Problems on High Dimensional Data by Prof Yongcheng Qi
- 15:50-16:10 Coffee Break& refreshment
- 16:10-17:00 Principle of a single big jump and its application by Prof Yuebao Wang
Topic 1: Some Testing Problems on High Dimensional Data
University of Minnesota Duluth
In the classical multivariate analysis, statistical methods have been developed mainly for data from designed experiments, and dimensions of the data are fixed. Nowadays, new technology has generated various types of high dimensional data whose dimensions can be very large compared with the sample sizes. In this case, some classical statistical approaches may not be applicable. In this talk, we review some examples with particular interests in multivariate normal distributions and reveal the limitations in applying those classical statistical methods such as likelihood ratio test statistics to high dimensional data and when they can be extended to test on high dimensional data. We will also introduce some recent developments of nonparametric methods for ultra-high dimensional data.
Prof. Yongcheng Qi is a statistics professor at University of Minnesota Duluth. His research interests include limiting theorems in probability and statistics, empirical likelihood methods, and extreme-value statistics, high dimensional data, and random matrix theory.
Topic 2: Principle of a single big jump and its application
Emeritus Professor of School of Mathematics, Soochow University
In this talk, we introduce the principle of a single big jump or Max-Sum equivalence. Further- more, we obtain a necessary and sufficient condition for the principle of a single big jump of product convolution. We propose an application of the obtained result to asymptotic study of the ruin probability in a discrete-time insurance risk model with stochastic returns. Finally, we highlight several questions for the further research.
Prof. Yuebao Wang is an Emeritus Professor of School of Mathematics, Soochow University. His research interests include limit theory, heavy tailed distribution theory, and its applications in risk models.