Dwarf spheroidal satellite galaxies (dSphs) of the Milky Way are considered ideal targets for

particle Dark Matter (DM) identification. Indirect detection strategies entail examining dSphs

in search for signals of annihilating or decaying DM, in the form of excess electrons or

gamma- and X-ray photons above the astrophysical background. To robustly compare model

predictions with the observed fluxes of such product particles, most analyses of astrophysical

data – which are generally frequentist – rely on estimating the abundance of DM by calculating

the so-called J-factor. This quantity is usually inferred from the kinematic properties of the

stellar population of a dSph using Jeans equation, commonly by means of Bayesian

techniques. Previous works have, therefore, combined different statistical methods when

analysing observational data from dSphs. In this thesis, I describe the development of a new,

fully-frequentist approach for constructing profile likelihood curves for the J-factor of dSphs.

I then use kinematic data from 20 dSphs to derive estimates of their maximum likelihood Jfactor

and its confidence intervals. The obtained J-factors and their uncertainties are in good

agreement with previous, Bayesian-derived values. This technique is validated using a

publicly available simulation suite, released by Gaia Challenge, by evaluating its coverage

and bias. The results of these tests indicate that the method possess good statistical properties.

The implications of these findings for DM searches are discussed, together with future

improvements and extensions of this technique.