One of my main areas of research interest is the development of statistical models for analysing high dimensional data. The route that I take is to significantly reduce the dimension of the problem without losing the important information contained in the data. In particular, I am interested in analysing high throughput bioinformatics data for the detection of potential biomarkers under the regularization (or, penalization) method.
Secondly, I am interested in developing a robust and/or efficient modelling procedures by introducing case-specific parameters which enable one to moderate the effect of each observation on the inference. The additional case-specific parameters must be penalized through a specific penalty that is tailored to a certain purpose of improving the robustness and/or efficiency of the inference. Application of case-specific parameters to robust models such as quantile regression enable one to make the procedures more efficient, and to efficient models such as least squares method, can bring certain degree of robustness.
The mentioned areas can be categorized as constructing new statistical models. On the other hand, the performance of existing statistical models can be significantly improved by bettering the model selection method. Thus, I also focus on developing new model selection methods for various classes of statistical models especially under high dimensional model and quantile regression. I am especially interested in developing consistent model selection procedures when the number of parameter (p) is greater than the number of sample size (n) and both p and n diverge
