  Fourier analysis and power spectrum estimation of the cosmic microwave
background anisotropy on an incompletely sampled sky developed by Gorski (1994)
has been applied to the high-latitude portion of the 4-year COBE DMR 31.5, 53
and 90 GHz sky maps. Likelihood analysis using newly constructed Galaxy cuts
(extended beyond |b| = 20deg to excise the known foreground emission) and
simultaneously correcting for the faint high latitude galactic foreground
emission is conducted on the DMR sky maps pixelized in both ecliptic and
galactic coordinates. The Bayesian power spectrum estimation from the
foreground corrected 4-year COBE DMR data renders n ~ 1.2 +/- 0.3, and
Q_{rms-PS} ~ 15.3^{+3.7}_{-2.8} microK (projections of the two-parameter
likelihood). These results are consistent with the Harrison-Zel'dovich n=1
model of amplitude Q_{rms-PS} ~ 18 microK detected with significance exceeding
14sigma (dQ/Q < 0.07). (A small power spectrum amplitude drop below the
published 2-year results is predominantly due to the application of the new,
extended Galaxy cuts.)
