A0264
Title: Completely pivotal estimation in multivariate response linear regression models
Authors: Guo Yu - University of California Santa Barbara (United States) [presenting]
Abstract: Despite the vast literature on sparse multivariate response linear regression models, most current methods require a known or explicit estimate of the dependence structure among the random errors. As a result, these methods hinge on computationally expensive methods (e.g., cross-validation) to determine the proper level of regularization. A completely pivotal framework is proposed for the sparse multivariate response linear regression model. The method estimates the coefficient matrix using a model-agnostic regularization parameter that does not depend on either the covariance matrix or the tail conditions of the random errors. In this sense, the proposal is completely tuning-free. Computationally, the estimator is a solution to a convex second-order cone program, which can be solved efficiently. Theoretically, the proposed estimator achieves favorable estimation error rates under mild conditions and could use a second-stage enhancement with non-convex penalties. Through comprehensive numerical studies, the method demonstrates promising statistical performance. Remarkably, the method exhibits strong robustness to the violation of the Gaussian assumption and significantly outperforms competing methods in the heavy-tailed settings.
