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

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.