Cosmic microwave background anisotropy power spectrum statistics for high precision cosmology

As the era of high precision cosmology approaches, the empirically determined power spectrum of the microwave background anisotropy Cₗ will provide a crucial test for cosmological theories. We present an exact semianalytic framework for the study of the sampling statistics of the Cₗ resulting from observations with partial sky coverage and anisotropic noise distributions. This includes space-borne, air-borne, and ground-based experiments. We apply this theory to demonstrate its power for constructing fast and unbiased approximate methods for the joint estimation of cosmological parameters. Further applications, such as a test for possible non-Gaussianity of the underlying theory and a ``poor man's power spectrum estimator'' are suggested. An appendix derives recursion relations for the efficient computation of the couplings between spherical harmonics on the cut sky.