Seminar Vol. 142
Title: A New Scope of Penalized Empirical Likelihood With High-Dimensional Estimating Equations
Speaker: Jinyuan Chang, Southwestern University of Finance and Economics
Time: April 15th, 2019 15:00–16:30
Venue: Conference Room 106B, Zhonghui Building (IESR, JNU College of Economics)
About the speaker:
Jinyuan Chang is a Professor and the Executive Director of the Joint Lab of Data Science and Business Intelligence at Southwestern University of Finance and Economics (SWUFE), China. He also serves on the Expert Advisory Committee of Sichuan Statistics Bureau. Before joining SWUFE in 2017, he was a Research Fellow at School of Mathematics and Statistics, The University of Melbourne, Australia. In 2013, he earned a Ph.D. in Statistics from Peking University. Jinyuan Chang's research mainly centers on high dimensional data analysis, empirical likelihood and its applications, financial econometrics, and functional data analysis. He has widely published in international journals like Annals of Statistics, Biometrika, and Journal of Econometrics. In addition, Jinyuan Chang is an Associate Editor of Statistica Sinica, Journal of the Royal Statistical Society Series, Journal of Business & Economic Statistics, and serves on the Editorial Board of Chinese Journal of Applied Probability and Statistics (Chinese).
Abstract:
Statistical methods with empirical likelihood (EL) are appealing and effective especially in conjunction with estimating equations for flexibly and adaptively incorporating data information. It is known that EL approaches encounter difficulties when dealing with high-dimensional problems. To overcome the challenges, we begin our study with investigating high-dimensional EL from a new scope targeting at high-dimensional sparse model parameters. We show that the new scope provides an opportunity for relaxing the stringent requirement on the dimensionality of the model parameters. Motivated by the new scope, we then propose a new penalized EL by applying two penalty functions respectively regularizing the model parameters and the associated Lagrange multiplier in the optimizations of EL. By penalizing the Lagrange multiplier to encourage its sparsity, a drastic dimension reduction in the number of estimating equations can be achieved. Most attractively, such a reduction in dimensionality of estimating equations can be viewed as a selection among those high-dimensional estimating equations, resulting in a highly parsimonious and effective device for estimating high-dimensional sparse model parameters. Allowing both the dimensionalities of model parameters and estimating equations growing exponentially with the sample size, our theory demonstrates that our new penalized EL estimator is sparse and consistent with asymptotically normally distributed nonzero components. Numerical simulations and a real data analysis show that the proposed penalized EL works promisingly.
