Mr Leshun Xu
PhD, MSc and BSc in Applied Mathematics (Jilin University)
Leshun Xu joined the Statistics Department as a PhD student in 2013. To keep pace with the new era of information and big data, he extended his interest into statistics and started his second PhD at UoA, the birth place of R language.
Before he took part in the fantastic research group here, he gained research experience and teaching experience from three universities, Jilin University, Nanjing Normal University and Northwest A & F University. He also harvested two years’ experience, from 2001 to 2003, as a software engineer in Dalian Hi-Think Corporation.
Currently, besides doing PhD research, he works as a tutor at the Department for undergraduate students who are studying Stats 10x (Introduction of Statistics), Stats 125 (Probability and Its Applications), Stats 20x (Data Analysis) and Stats 330 (Advanced Statistical Modelling).
Professor Alan Lee (Principal Supervisor)
Professor Chris Wild (Associate Supervisor)
Professor Thomas Lumley (Associate Supervisor)
Emeritus Professor Alastair Scott
Research | Current
Leshun’s research topic is “Asymptotics for Survey Data Based on Spatial Processes”, which is supported by the Marsden Foundation.
In this research, we will prove some central limit theorems for survey data, where the model-based sample frame is from a superpopulation generated by a random field. In order to obtain a central limit theorem, strong mixing conditions on the fields will be combined with conditions on the sampling, e.g. conditions on stratified or clustered samples. As a further consideration on empirical processes, this result could be extended to a new Donsker’s theorem.
Our results will contribute to some real-world problems, e.g. in some surveys, we can divide the field into smaller districts as clusters. We then sample clusters at random, and again, randomly select sample points within the selected clusters. The correlation of sample points within one cluster can be described by mixing coefficients, which is related to the size of the cluster. In addition, it would be reasonable to take the correlations between clusters into consideration. Both correlations can be taken into account in our results. Practically, our results can be applied to household surveys, labour force surveys, marketing surveys and so on.