not possible and some form of regularisation is required. @hansen02b advocate using likelihood methods, while @chon04 make use of correlation functions as an intermediate data product. A notable feature of the latter approach is that the inversion is constructed so that electric and magnetic polarization power is not mixed in the mean. Pseudo-$C_l$ methods have now been applied to a number of real data sets, both for temperature [@netterfield02; @hinshaw03] and polarization analyses [@kogut03; @ponthieu05].

Despite the attention that pseudo-$C_l$ techniques have received, relatively little work has been done on trying to *understand* their error properties. This paper aims to fill that gap by providing the basis for a reliable, semi-analytic error analysis technique for CMB polarization power spectrum estimates obtained with pseudo-$C_l$ methods. This extends earlier analytic work that discusses temperature anisotropies only [@hinshaw03; @efstathiou04], and the recent thesis work by one of us [@chon_thesis] where both temperature and polarization are considered. A significant complication that arises for polarized data is the mixing of $E$ and $B$ modes for observations covering only part of the sky [@lewis02; @bunn03]. We develop approximations to the pseudo-$C_l$ sample covariances, taking this mixing into account at leading order for maps with smoothly-apodized edges. 