Maximum-Likelihood Analysis of the COBE Angular Correlation Function

We have used maximum-likelihood estimation to determine the quadrupole amplitude $Q_{\rm rms-PS}$ and the spectral index $n$ of the density fluctuation power spectrum at recombination from the \cobe\ DMR data. We find a strong correlation between the two parameters of the form $Q_{\rm rms-PS}=(15.7\pm 2.6)\exp[0.46(1-n)]\mk$ for fixed $n$. Our result is slightly smaller than and has a smaller statistical uncertainty than the 1992 estimate of Smoot et al.