  Recovering the original spectral lineshapes from data obtained by instruments
with extended transmission profiles is a basic tenet in spectroscopy. By using
the moments of the measured lines as basic variables, we turn the problem into
a linear inversion. However, when only a finite number of these moments are
relevant, the rest of them act as nuisance parameters. These can be taken into
account with a semiparametric model, which allows us to establish the ultimate
bounds on the precision attainable in the estimation of the moments of
interest. We experimentally confirm these limits with a simple ghost
spectroscopy demonstration.
