COMMENTS ON THE STATISTICAL-ANALYSIS OF EXCESS VARIANCE IN THE COBE DIFFERENTIAL MICROWAVE RADIOMETER MAPS

Cosmic anisotropy produces an excess variance sigma(sky)2 in the DELTA T maps produced by the Differential Microwave Radiometer (DMR) on COBE that is over and above the instrument noise. After smoothing to an ef fective resolution of 10-degrees, this excess, sigma(sky)10-degrees, p rovides an estimate for the amplitude of the primordial density pertur bation power spectrum with a cosmic uncertainty of only 12%. We employ detailed Monte Carlo techniques to express the amplitude derived from this statistic in terms of the universal rms quadrupole amplitude, [Q (RMS)2]0.5. The effects of monopole and dipole subtraction and the non -Gaussian shape of the DMR beam cause the derived [Q(RMS)2]0.5 to be 5 %-10% larger than would be derived using simplified analytic approxima tions. We also investigate the properties of two other map statistics: the actual quadrupole and the Boughn-Cottingham statistic. Both the s igma(sky)(10-degrees) statistic and the Boughn-Cottingham statistic ar e consistent with the [Q(RMS)2] = 17 +/- 5 muK reported by Smoot et al . (1992) and Wright et al. (1992).