  We study two-neutrino ($2\nu\beta\beta$) and neutrinoless double-$\beta$
($0\nu\beta\beta$) decays in the nuclear shell model and proton-neutron
quasiparticle random-phase approximation (pnQRPA) frameworks. Calculating the
decay half-life of several dozens of nuclei ranging from calcium to xenon with
the shell model, and of $\beta\beta$ emitters with a wide range of
proton-neutron pairing strengths in the pnQRPA, we observe good linear
correlations between $2\nu\beta\beta$- and $0\nu\beta\beta$-decay nuclear
matrix elements for both methods. We then combine the correlations with
measured $2\nu\beta\beta$-decay half-lives to predict $0\nu\beta\beta$-decay
matrix elements with theoretical uncertainties based on our systematic
calculations. Our results include two-body currents and the short-range
$0\nu\beta\beta$-decay operator.
