标题： 协变量高缺失率数据的半监督学习方法填补 显示英文标题

标题： Imputations for High Missing Rate Data in Covariates via Semi-supervised Learning Approach

摘要： 数据收集技术的进步和数据资源的异质性可能导致变量上出现高比例的缺失观测值，例如块状缺失数据。 在缺失数据场景下，传统的方法如简单平均、$k$-最近邻、多重和回归插补可能会导致结果不稳定或无法计算。 受半监督学习概念的启发（参见，例如Zhu和Goldberg，2009和Chapelle等，2010），我们提出了一种新方法，用于填补具有高缺失率的协变量中的缺失值。 具体来说，我们将任何协变量中的缺失和非缺失个体分别视为未标记和已标记的目标输出，并将它们相应的响应视为未标记和已标记的输入。 这种创新设置使我们能够在不施加任何模型假设的情况下插补大量缺失数据。 此外，对于连续协变量，得到的插补具有闭合形式，并且可以高效计算。 类似的过程也适用于离散协变量。 我们进一步采用非参数技术来展示插补协变量的理论性质。 通过模拟研究和一个在线消费金融的例子，展示了所提出方法的实用性。 显示英文摘要

摘要： Advancements in data collection techniques and the heterogeneity of data resources can yield high percentages of missing observations on variables, such as block-wise missing data. Under missing-data scenarios, traditional methods such as the simple average, $k$-nearest neighbor, multiple, and regression imputations may lead to results that are unstable or unable be computed. Motivated by the concept of semi-supervised learning (see, e.g., Zhu and Goldberg, 2009 and Chapelle et al., 2010), we propose a novel approach with which to fill in missing values in covariates that have high missing rates. Specifically, we consider the missing and non-missing subjects in any covariate as the unlabelled and labelled target outputs, respectively, and treat their corresponding responses as the unlabelled and labelled inputs. This innovative setting allows us to impute a large number of missing data without imposing any model assumptions. In addition, the resulting imputation has a closed form for continuous covariates, and it can be calculated efficiently. An analogous procedure is applicable for discrete covariates. We further employ the nonparametric techniques to show the theoretical properties of imputed covariates. Simulation studies and an online consumer finance example are presented to illustrate the usefulness of the proposed method.