  Matching a nonprobability sample to a probability sample is one strategy both
for selecting the nonprobability units and for weighting them. This approach
has been employed in the past to select subsamples of persons from a large
panel of volunteers. One method of weighting, introduced here, is to assign a
unit in the nonprobability sample the weight from its matched case in the
probability sample. The properties of resulting estimators depend on whether
the probability sample weights are inverses of selection probabilities or are
calibrated. In addition, imperfect matching can cause estimates from the
matched sample to be biased so that its weights need to be adjusted, especially
when the size of the volunteer panel is small. Calibration weighting combined
with matching is one approach to correcting bias and reducing variances. We
explore the theoretical properties of the matched and matched, calibrated
estimators with respect to a quasirandomization distribution that is assumed to
describe how units in the nonprobability sample are observed, a superpopulation
model for analysis variables collected in the nonprobability sample, and the
randomization distribution for the probability sample. Numerical studies using
simulated and real data from the 2015 US Behavioral Risk Factor Surveillance
Survey are conducted to examine the performance of the alternative estimators.
