  This paper presents theoretical results on combining non-probability and
probability survey samples through mass imputation, an approach originally
proposed by Rivers (2007) as sample matching without rigorous theoretical
justification. Under suitable regularity conditions, we establish the
consistency of the mass imputation estimator and derive its asymptotic variance
formula. Variance estimators are developed using either linearization or
bootstrap. Finite sample performances of the mass imputation estimator are
investigated through simulation studies and an application to analyzing a
non-probability sample collected by the Pew Research Centre.
