The Epoch of Reionization Window: I. Mathematical Formalism
  The 21 cm line provides a powerful probe of astrophysics and cosmology at
high redshifts, but unlocking the potential of this probe requires the robust
mitigation of foreground contaminants that are typically several orders of
magnitude brighter than the cosmological signal. Recent simulations and
observations have shown that the smooth spectral structure of foregrounds
combines with instrument chromaticity to contaminate a "wedge"-shaped region in
cylindrical Fourier space. While previous efforts have explored the suppression
of foregrounds within this wedge, as well as the avoidance of this highly
contaminated region, all such efforts have neglected a rigorous examination of
the error statistics associated with the wedge. Using a quadratic estimator
formalism applied to the interferometric measurement equation, we provide a
framework for such a rigorous analysis (incorporating a fully covariant
treatment of errors). Additionally, we find that there are strong error
correlations at high spatial wavenumbers that have so far been neglected in
sensitivity derivations. These error correlations substantially degrade the
sensitivity of arrays relying on contributions from long baselines, compared to
what one would estimate assuming uncorrelated errors.
