Research Interest

Statistical Methods in Psychometric Measurement

The first part of my research activities is concerned with statistical and psychometric problems arising from educational and psychological assessment. It involves latent structure modeling of item response data and statistical analysis thereof. In particular, we have addressed some fundamental issues related to Q-matrix based diagnostic classification models, which have witnessed tremendous surge of interest in recent years.

Jingchen Liu, Gongjun Xu and Zhiliang Ying (2012). Theory of Self-Learning Q-matrix. Bernoulli to appear.
Jingchen Liu, Gongjun Xu and Zhiliang Ying (2012). Data-driven learning of Q-matrix. Applied Psychological Measurement. 36(7), 548-564.

Rare Event Analysis and Large Deviations

My current research focuses on the asymptotic analysis and efficient simulation of rare events related to Gaussian random fields, and in particular, their exponential integrals. Consider a Gaussian random field {f(t): tin T} . We are interested in tail probability $P(int_T e^{f(t)} dt >b)$ as brightarrowinfty .

Jingchen Liu and Gongjun Xu (2012). Some Asymptotic Results of Gaussian Random Fields with Varying Mean Functions and the Associated Processes. Annals of Statistics. 40(1), 262-293.
Jingchen Liu and Gongjun Xu (2012). On the Density Functions of Integrals of Gaussian Random Fields. Advances in Applied Probability to appear.
Jingchen Liu and Gongjun Xu (2012). Rare-event Simulation for Exponential Integrals of Smooth Gaussian Processes. Proceedings of the 2012 Winter Simulation Conference.
Jingchen Liu and Gongjun Xu. Efficient Simulations for the Exponential Integrals of Hölder Continuous Gaussian Random Fields. Under revision.
Jingchen Liu and Gongjun Xu. On the Conditional Distributions and the Efficient Simulations of Exponential Integrals of Gaussian Random Fields. Submitted.

Survival Analysis

I have been working on sequential and adaptive designs of clinical trials, spatially correlated failure time data, and change-point problems.

Xiaolong Luo, Gongjun Xu and Zhiliang Ying. Sequential Analysis of Cox Model under Response Adaptive Allocation. Under revision.