Deliang Dai

Basic Statistics I

Basic Statistics II

Multivariate statistical analysis and its related methods are widely used in various areas when one gets more than one variable in the analysis. Many multivariate analyses assume that the random variables are normally distributed. But this restriction is violated frequently in the reality due to some practical issues, for example, the outlier. Therefore, outlier detection has become an important and necessary step in all kinds of analysis. Much attention was paid in developing different methods to detect the outlier more efficiently during the last few decades.

Due to the fast development of the Internet of Things (IoT), the availability of data increasing drastically. It brings more challenges and opportunities: the high-dimensional statistical analysis. Under the context of high-dimensional data, some new and more powerful methods are needed to be investigated to fit the new needings.  

My research interests start with developing the outlier detection methods, for example, Mahalanobis distance under high dimensional settings. Mahalanobis distance consists of two parts: mean and covariance. These two parameters are used not only to build the Mahalanobis distance but also to calibrate various statistics such as the Normal distribution and t-test statistics, to name but a few. From this point, my research is extended to different covariance matrix estimation related methods especially for the high-dimensional setting, here high dimensional implies when the number of variables is larger than the number of observations. I'm also interested in the empirical applications of machine learning/data science with energy industry-related topics.