  Administrative data, or non-probability sample data, are increasingly being
used to obtain official statistics due to their many benefits over survey
methods. In particular, they are less costly, provide a larger sample size, and
are not reliant on the response rate. However, it is difficult to obtain an
unbiased estimate of the population mean from such data due to the absence of
design weights. Several estimation approaches have been proposed recently using
an auxiliary probability sample which provides representative covariate
information of the target population. However, when this covariate information
is high-dimensional, variable selection is not a straight-forward task even for
a subject matter expert. In the context of efficient and doubly robust
estimation approaches for estimating a population mean, we develop two data
adaptive methods for variable selection using the outcome adaptive LASSO and a
collaborative propensity score, respectively. Simulation studies are performed
in order to verify the performance of the proposed methods versus competing
methods. Finally, we presented an anayisis of the impact of Covid-19 on
Canadians.
