  It is likely that the observed distribution of the microwave background
temperature over the sky is only one realization of the underlying random
process associated with cosmological perturbations of quantum-mechanical
origin. If so, one needs to derive the parameters of the random process, as
accurately as possible, from the data of a single map. These parameters are of
the utmost importance, since our knowledge of them would help us to reconstruct
the dynamical evolution of the very early Universe. It appears that the lack of
ergodicity of a random process on a 2-sphere does not allow us to do this with
arbitrarily high accuracy. We are left with the problem of finding the best
unbiased estimators of the participating parameters. A detailed solution to
this problem is presented in this article. The theoretical error bars for the
best unbiased estimates are derived and discussed.
