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严晓东——山东大学
Covariate-specified group structure recovery for high-dimensional regression
嘉宾介绍
严晓东(Xiaodong Yan)，山东大学经济学院副研究员(Associate Professor at School of Economics, Shandong University)。研究方向(Research Interests)：计量经济(Econometrics)、计量金融(Quantitative Finance)、风险管理(Risk Management)、大数据分析(Big Data Analysis)、学习经历(Studying Experience)。
报告摘要
This paper studies integrative analysis of multiple units in the context of high-dimensional linear regression. We consider the case where a fraction of the covariates pose different effects on the responses across various units, e.g., some covariate-specific coefficients are the same for all the units, while others have a grouping structure. We propose a double penalized least squares approach by combining quadratic loss function with a fusion penalty term to penalize the difference between any two units’ coefficients of the same covariate for identifying latent grouping structure, as well as a sparsity penalty to detect nonzero effects. Without the need of knowing the grouping structure of every variable among the data units and the sparsity construction within the variables, the proposed double penalized procedure can automatically recover sorts of structures of covariate-specific effects such as heterogeneous, homogeneous and sparsity, and estimate the parameters simultaneously. We proceed the alternating direction method of multipliers algorithm (ADMM) through effectively utilizing the storage and reading of the datasets, and demonstrate convergence of the proposed procedure. We show that the proposed estimator enjoys the oracle property in recovering the underlying covariate-specific structure of heterogeneous, homogeneous and sparsity. Simulation studies demonstrate the good performance of the new method with finite samples, and a real data example is provided for illustration.
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