title: Adaptive Estimation with Partially Overlapping Models.
abstract: In many problems, one has several models of interest that capture key parameters describing the distribution of the data. Partially overlapping models are taken as models in which at least one covariate effect is common to the models. A priori knowledge of such structure enables efficient estimation of all model parameters. However, in practice, this structure may be unknown. We propose adaptive composite M-estimation (ACME) for partially overlapping models using a composite loss function, which is a linear combination of loss functions defining the individual models. Penalization is applied to pairwise differences of parameters across models, resulting in data driven identification of the overlap structure. Further penalization is imposed on the individual parameters, enabling sparse estimation in the regression setting. The recovery of the overlap structure enables more efficient parameter estimation. An oracle result is established. Simulation studies illustrate the advantages of ACME over existing methods that fit individual models separately or make strong a priori assumption about the overlap structure.
authors.affiliation: Department of Statistics, Department of Biostatistics and Medical Informatics, The University of Wisconsin-Madison, Madison, WI 53706, U.S.A.
authors.forename: Sunyoung
authors.initials: S
authors.lastname: Shin
authors.affiliation: Department of Biostatistics, Department of Statistics and Operations Research, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, U.S.A.
authors.forename: Jason
authors.initials: J
authors.lastname: Fine
authors.affiliation: Department of Statistics and Operations Research, Department of Biostatistics, Carolina Center for Genome Sciences, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, U.S.A.
authors.forename: Yufeng
authors.initials: Y
authors.lastname: Liu
keywords: Composite loss function; Lasso; Model selection; Oracle property; Overlapping; Penalization; Sparsity