報告題目：Sparse composite quantile regression with consistent parameter tuning in ultrahigh dimensions
報告時間: 2018年7月8日（周日）10:00－11:00
報告地點：北辰校區理學院（西教五）416
報告嘉賓：Dr.Yuwen Gu（University of Connecticut）
Abstract: Composite quantile regression (CQR) provides efficient estimation of the coefficients in linear models, regardless of the error distributions. We consider penalized CQR for both variable selection and efficient coefficient estimation in a linear model under ultrahigh dimensionality and possibly heavy-tailed error distribution. Both lasso and folded concave penalties are discussed. An L2 risk bound is derived for the lasso estimator to establish its estimation consistency and strong oracle property of the folded concave penalized CQR is shown for a feasible solution via the LLA algorithm. The nonsmooth nature of the penalized CQR poses great numerical challenges for high-dimensional data. We provide a unified and effective numerical optimization algorithm for computing penalized CQR via alternating direction method of multipliers (ADMM). We demonstrate the superior efficiency of penalized CQR estimator, as compared to the penalized least squares estimator, through simulated data under various error distributions. For folded concave penalized quantile regression, we also show consistent parameter tuning using a high-dimensional BIC type information criterion. Simulation studies are carried out to show its superior finite-sample performance.
嘉賓簡介：Dr. Yuwen Gu is now an assistant professor in the Department of Statistics at the University of Connecticut. He received his PhD in Statistics from the University of Minnesota in 2017. Dr. Gu’s research interests include high-dimensional statistical inference, variable selection, model combination, nonparametric statistics, causal inference, and large-scale optimization. His current research projects study several non-standard regression techniques for high-dimensional data analysis. These methods have unique advantages over the standard least squares regression and have applications in large-scale data that exhibit heterogeneity or heavy tails. He is also working on applications of statistical learning and causal inference methods in social and economic data.
