  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.
