  The statistical matching problem is a data integration problem with
structured missing data. The general form involves the analysis of multiple
datasets that only have a strict subset of variables jointly observed across
all datasets. The simplest version involves two datasets, labelled A and B,
with three variables of interest $X, Y$ and $Z$. Variables $X$ and $Y$ are
observed in dataset A and variables $X$ and $Z$ are observed in dataset $B$.
Statistical inference is complicated by the absence of joint $(Y, Z)$
observations. Parametric modelling can be challenging due to identifiability
issues and the difficulty of parameter estimation. We develop computationally
feasible procedures for the statistical matching of non-Gaussian data using
suitable data augmentation schemes and identifiability constraints.
Nearest-neighbour imputation is a common alternative technique due to its ease
of use and generality. Nearest-neighbour matching is based on a conditional
independence assumption that may be inappropriate for non-Gaussian data. The
violation of the conditional independence assumption can lead to improper
imputations. We compare model based approaches to nearest-neighbour imputation
on a number of flow cytometry datasets and find that the model based approach
can address some of the weaknesses of the nonparametric nearest-neighbour
technique.
