How to measure CMB polarization power spectra without losing information -art. no. 063001

We present a method for measuring CMB polarization power spectra given inco mplete sky coverage and test it with simulated examples such as Boomerang 2 001 and MAP. By augmenting the quadratic estimator method with an additiona l step, we find that the E and B power spectra can be effectively disentang led on angular scales substantially smaller than the width of the sky patch in the narrowest direction. We find that the basic quadratic and maximum-l ikelihood methods display an unneccesary sensitivity to systematic errors w hen T-E cross-correlation is involved. and show how this problem can be eli minated at negligible cost in increased error bars. We also test numericall y the widely used approximation that sample variance scales inversely with sky coverage, and find it to be an excellent approximation on scales substa ntially smaller than the sky patch.