The average structural evolution of massive galaxies can be reliably
  estimated using cumulative galaxy number densities
  Galaxy evolution can be studied observationally by linking progenitor and
descendant galaxies through an evolving cumulative number density selection.
This procedure can reproduce the expected evolution of the median stellar mass
from abundance matching. However, models predict an increasing scatter in main
progenitor masses at higher redshifts, which makes galaxy selection at the
median mass unrepresentative. Consequently, there is no guarantee that the
evolution of other galaxy properties deduced from this selection are reliable.
Despite this concern, we show that this procedure approximately reproduces the
evolution of the average stellar density profile of main progenitors of M =
10^11.5 Msun galaxies, when applied to the EAGLE hydrodynamical simulation. At
z > 3.5 the aperture masses disagree by about a factor two, but this
discrepancy disappears when we include the expected scatter in cumulative
number densities. The evolution of the average density profile in EAGLE broadly
agrees with observations from UltraVISTA and CANDELS, suggesting an inside-out
growth history for these massive galaxies over 0 < z < 5. However, for z < 2
the inside-out growth trend is stronger in EAGLE. We conclude that cumulative
number density matching gives reasonably accurate results when applied to the
evolution of the mean density profile of massive galaxies.
