A0161
Title: Penalized sparse covariance regression with high dimensional covariates
Authors: Yuan Gao - Central University of Finance and Economics (China) [presenting]
Zhiyuan Zhang - Fudan University (China)
Xuening Zhu - Fudan University (China)
Zhanrui Cai - Iowa State University (United States)
Tao Zou - The Australian National University (Australia)
Hansheng Wang - Peking University (China)
Abstract: Covariance regression offers an effective way to model the large covariance matrix with the auxiliary similarity matrices. A sparse covariance regression (SCR) approach is proposed to handle the potentially high-dimensional predictors (i.e., similarity matrices). Specifically, the penalization method is used to identify the informative predictors and estimate their associated coefficients simultaneously. The Lasso estimator is first investigated, and subsequently, the folded concave penalized estimation methods (e.g., SCAD and MCP) are considered. However, the theoretical analysis of the existing penalization methods is primarily based on i.i.d. data, which is not directly applicable to the scenario. To address this difficulty, the non-asymptotic error bounds are established by exploiting the spectral properties of the covariance matrix and similarity matrices. Then, the estimation error bound is derived for the Lasso estimator, and the desirable oracle property of the folded concave penalized estimator is established. Extensive simulation studies are conducted to corroborate the theoretical results. The usefulness of the proposed method is also illustrated by applying it to a Chinese stock market dataset.
