  We demonstrate the feasibility to generate surrogates by Fourier-based
methods for an incomplete data set. This is performed for the case of a CMB
analysis, where astrophysical foreground emission, mainly present in the
Galactic plane, is a major challenge. The shuffling of the Fourier phases for
generating surrogates is now enabled by transforming the spherical harmonics
into a new set of basis functions that are orthonormal on the cut sky. The
results show that non-Gaussianities and hemispherical asymmetries in the CMB as
identified in several former investigations, can still be detected even when
the complete Galactic plane (|b| < 30{\deg}) is removed. We conclude that the
Galactic plane cannot be the dominant source for these anomalies. The results
point towards a violation of statistical isotropy.
