Estimates of multipolar coefficients for searching for cosmic ray anisotropies with non-uniform or partial sky coverage

We study the possibility of extracting the multipolar moments of an underlying distribution from a set of cosmic rays observed with non-uniform or even partial sky coverage. We show that if the degree is assumed to be upper bounded by L , each multipolar moment can be recovered whatever the coverage, but with a variance increasing exponentially with the bound L if the coverage is zero somewhere. Despite this limitation, we show the possibility of testing predictions of a model without any assumption on L by building an estimate of the covariance matrix seen through the exposure function.