A General M-estimation Theory in Semi-Supervised Framework

• 成果类型: Article
• 署名作者: Song, Shanshan; Lin, Yuanyuan; Zhou, Yong
• 署名单位: Chinese University of Hong Kong; East China Normal University; East China Normal University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2023.2169699
• 发表日期: 2024
• 页码: 1065-1075
• 关键词: Model misspecification; quantile regression; linear-regression; CONSEQUENCES; efficient; inference

摘要

We study a class of general M-estimators in the semi-supervised setting, wherein the data are typically a combination of a relatively small labeled dataset and large amounts of unlabeled data. A new estimator, which efficiently uses the useful information contained in the unlabeled data, is proposed via a projection technique. We prove consistency and asymptotic normality, and provide an inference procedure based on K -fold cross-validation. The optimal weights are derived to balance the contributions of the labeled and unlabeled data. It is shown that the proposed method, by taking advantage of the unlabeled data, produces asymptotically more efficient estimation of the target parameters than the supervised counterpart. Supportive numerical evidence is shown in simulation studies. Applications are illustrated in analysis of the homeless data in Los Angeles. for this article are available online.