  We present a method to infer on joint regression coefficients obtained from
marginal regressions using a reference panel. This type of scenario is common
in genetic fine-mapping, where the estimated marginal associations are reported
in genomewide association studies (GWAS), and a reference panel is used for
inference on the association in a joint regression model. We show that ignoring
the uncertainty due to the use of a reference panel instead of the original
design matrix, can lead to a severe inflation of false discoveries and a lack
of replicable findings. We derive the asymptotic distribution of the estimated
coefficients in the joint regression model, and show how it can be used to
produce valid inference. We address two settings: inference within regions that
are pre-selected, as well as within regions that are selected based on the same
data. By means of real data examples and simulations we demonstrate the
usefulness of our suggested methodology.
