A General M-estimation Theory in Semi-Supervised Framework
研究半监督场景下的一般M估计量，提出利用投影技术结合少量标注和大量未标注数据的新估计量，证明其一致性和渐近正态性，并通过交叉验证进行推断，在洛杉矶无家可归者数据分析中展示应用。
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. Supplementary materials for this article are available online.