Planck intermediate results. XVI. Profile likelihoods for cosmological
  parameters
  We explore the 2013 Planck likelihood function with a high-precision
multi-dimensional minimizer (Minuit). This allows a refinement of the
Lambda-cdm best-fit solution with respect to previously-released results, and
the construction of frequentist confidence intervals using profile likelihoods.
The agreement with the cosmological results from the Bayesian framework is
excellent, demonstrating the robustness of the Planck results to the
statistical methodology. We investigate the inclusion of neutrino masses, where
more significant differences may appear due to the non-Gaussian nature of the
posterior mass distribution. By applying the Feldman--Cousins prescription, we
again obtain results very similar to those of the Bayesian methodology.
However, the profile-likelihood analysis of the CMB combination
(Planck+WP+highL) reveals a minimum well within the unphysical negative-mass
region. We show that inclusion of the Planck CMB-lensing information
regularizes this issue, and provide a robust frequentist upper limit $M_\nu <
0.26 eV$ ($95%$ confidence) from the CMB+lensing+BAO data combination.
