  We apply the theory of semiparametric estimation to a Hong-Ou-Mandel
interference experiment with a spectrally entangled two-photon state generated
by spontaneous parametric downconversion. Thanks to the semiparametric approach
we can evaluate the Cram\'er-Rao bound and find an optimal estimator for a
particular parameter of interest without assuming perfect knowledge of the
two-photon wave function, formally treated as an infinity of nuisance
parameters. In particular, we focus on the estimation of the Hermite-Gauss
components of the marginal symmetrised wavefunction, whose Fourier transform
governs the shape of the temporal coincidence profile. We show that negativity
of these components is an entanglement witness of the two-photon state.
