Unified Optimal Model Averaging with a General Loss Function based on Cross-Validation

• 成果类型: Article
• 署名作者: Yu, Dalei; Zhang, Xinyu; Liang, Hua
• 署名单位: Xi'an Jiaotong University; Chinese Academy of Sciences; University of Science & Technology of China, CAS; Chinese Academy of Sciences; Nanjing Institute of Geology & Paleontology, CAS; Academy of Mathematics & System Sciences, CAS; George Washington University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2025.2487215
• 发表日期: 2025-10-02
• 页码: 2697-2708
• 关键词: Asymptotic Optimality; Consistency; misspecification; Nonnormal/nonindependent data; Spatial Data; estimating equations; information criterion; likelihood-estimation; quasi-likelihood; selection; distributions

摘要

Studying unified model averaging estimation for situations with complicated data structures, we propose a novel model averaging method based on cross-validation (MACV). MACV unifies a large class of new and existing model averaging estimators and covers a very general class of loss functions. Furthermore, to reduce the computational burden caused by the conventional leave-subject/one-out cross-validation, we propose a SEcond-order-Approximated Leave-one/subject-out (SEAL) cross-validation, which largely improves the computation efficiency. In the context of nonindependent and non-identically distributed random variables, we establish the unified theory for analyzing the asymptotic behaviors of the proposed MACV and SEAL methods, where the number of candidate models is allowed to diverge with sample size. To demonstrate the breadth of the proposed methodology, we exemplify four optimal model averaging estimators under four important situations, that is, longitudinal data with discrete responses, within-cluster correlation structure modeling, conditional prediction in spatial data, and quantile regression with a potential correlation structure. We conduct extensive simulation studies and analyze real-data examples to illustrate the advantages of the proposed methods. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.