A0568
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 for the sparse multivariate response linear regression model is proposed. Our method estimates the coefficient matrix using a model-agnostic regularization parameter that does not depend on the covariance matrix or the tail conditions of the random errors. In this sense, our proposal is completely tuning-free. Computationally, our estimator is a solution to a convex second-order cone program, which can be solved efficiently. Theoretically, the proposed estimator achieves favourable estimation error rates under mild conditions and could use a second-stage enhancement with non-convex penalties. Through comprehensive numerical studies, our method demonstrates promising statistical performance. Remarkably, our method exhibits strong robustness to violating the Gaussian assumption and significantly outperforms competing methods in heavy-tailed settings.
