  We study the angular power spectrum estimate in order to search for large
scale anisotropies in the arrival directions distribution of the highest-energy
cosmic rays. We show that this estimate can be performed even in the case of
partial sky coverage and validated over the full sky under the assumption that
the observed fluctuations are statistically spatial stationary. If this
hypothesis - which can be tested directly on the data - is not satisfied, it
would prove, of course, that the cosmic ray sky is non isotropic but also that
the power spectrum is not an appropriate tool to represent its anisotropies,
whatever the sky coverage available. We apply the method to simulations of the
Pierre Auger Observatory, reconstructing an input power spectrum with the
Southern site only and with both Northern and Southern ones. Finally, we show
the improvement that a full-sky observatory brings to test an isotropic
distribution, and we discuss the sensitivity of the Pierre Auger Observatory to
large scale anisotropies.
