  The National Health and Nutrition Examination Survey (NHANES) studies the
nutritional and health status over the whole U.S. population with comprehensive
physical examinations and questionnaires. However, survey data analyses become
challenging due to inevitable missingness in almost all variables. In this
paper, we develop a new imputation method to deal with multivariate missingness
at random using matrix completion. In contrast to existing imputation schemes
either conducting row-wise or column-wise imputation, we treat the data matrix
as a whole which allows exploiting both row and column patterns to impute the
missing values in the whole data matrix at one time. We adopt a
column-space-decomposition model for the population data matrix with
easy-to-obtain demographic data as covariates and a low-rank structured
residual matrix. A unique challenge arises due to lack of identification of
parameters in the sample data matrix. We propose a projection strategy to
uniquely identify the parameters and corresponding penalized estimators, which
are computationally efficient and possess desired statistical properties. The
simulation study shows that the doubly robust estimator using the proposed
matrix completion for imputation has smaller mean squared error than other
competitors. To demonstrate practical relevance, we apply the proposed method
to the 2015-2016 NHANES Questionnaire Data.
