Adaptive Composite M-Estimation for Partially Overlapping Models

• Activity Number: 651
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Sunyoung Shin*+ and Jason Fine and Yufeng Liu
• Companies: The University of North Carolina Chapel Hill and The University of North Carolina Chapel Hill and The University of North Carolina
• Keywords: Penalization ; Oracle Propertie ; SCAD ; Lasso ; Quantile Regression

Abstract

Composite loss function, a weighted combination of multiple losses has been developed for efficient and robust estimation in regression. In the composite loss function, we introduce the notion of "partially overlapping models", where the multiple losses have the common parameters to some covariates. The paper proposes an adaptive composite M-estimation (ACME) in partially overlapping models for sparse and overlapping recovery. ACME adds two penalty terms to the composite loss: the regular penalty to each coefficient and the penalty to pairwise differences of coefficients to each covariate across models. ACME circumvents the model misspecification issue inherent in other composite loss based estimation methods. Further, ACME with theoretically optimal weight is as efficient as if the true sparsity and overlapping structure is known in advance. Simulation studies and baseball data analysis illustrate that ACME has advantages over other existing methods.