  Line-of-sight integrals of the squared density, commonly called the J-factor,
are essential for inferring dark matter annihilation signals. The J-factors of
dark matter-dominated dwarf spheroidal satellite galaxies (dSphs) have
typically been derived using Bayesian techniques, which for small data samples
implies that a choice of priors constitutes a non-negligible systematic
uncertainty. Here we report the development of a new fully frequentist approach
to construct the profile likelihood of the J-factor. Using stellar kinematic
data from several classical and ultra-faint dSphs, we derive the maximum
likelihood value for the J-factor and its confidence intervals. We validate
this method, in particular its bias and coverage, using simulated data from the
Gaia Challenge. We find that the method possesses good statistical properties.
The J-factors and their uncertainties are generally in good agreement with the
Bayesian-derived values, with the largest deviations restricted to the systems
with the smallest kinematic datasets. We discuss improvements, extensions, and
future applications of this technique.
