  This paper introduces a novel error estimator for the Proper Generalized
Decomposition (PGD) approximation of parametrized equations. The estimator is
intrinsically random: It builds on concentration inequalities of Gaussian maps
and an adjoint problem with random right-hand side, which we approximate using
the PGD. The effectivity of this randomized error estimator can be arbitrarily
close to unity with high probability, allowing the estimation of the error with
respect to any user-defined norm as well as the error in some quantity of
interest. The performance of the error estimator is demonstrated and compared
with some existing error estimators for the PGD for a parametrized
time-harmonic elastodynamics problem and the parametrized equations of linear
elasticity with a high-dimensional parameter space.
