  We characterize a cosmic rest frame in which the monopole variation of the
spherically averaged nonlinear Hubble expansion is most uniform, under
arbitrary local Lorentz boosts of the central observer. Using the COMPOSITE
sample of 4534 galaxies, we identify a degenerate set of candidate minimum
nonlinear variation frames, which includes the rest frame of the Local Group
(LG) of galaxies, but excludes the standard Cosmic Microwave Background (CMB)
frame. Candidate rest frames defined by a boost from the LG frame close to the
plane of the galaxy have a statistical likelihood similar to the LG frame. This
may result from a lack of constraining data in the Zone of Avoidance. We extend
our analysis to the Cosmicflows-2 (CF2) sample of 8162 galaxies. While the
signature of a systematic boost offset between the CMB and LG frame averages is
still detected, the spherically averaged nonlinear expansion variation in all
rest frames is significantly larger in the CF2 sample than would be reasonably
expected. We trace this to the CF2 distances being reported without a
correction for inhomogeneous distribution Malmquist bias. Systematic
differences in the inclusion of the large SFI++ subsample into the COMPOSITE
and CF2 catalogues are analysed. Our results highlight the importance of a
careful treatment of Malmquist biases for future peculiar velocities studies,
including tests of the hypothesis of Wiltshire et al [Phys. Rev. D 88 (2013)
083529; arXiv:1201.5371] that a significant fraction of the CMB temperature
dipole may be nonkinematic in origin.
