We discuss the analytic properties of the cross-power spectrum estimator from multi-detector CMB anisotropy maps. The method is computationally convenient and it provides unbiased estimates under very broad assumptions. We also propose a new procedure to test for the presence of residual bias due to improper noise subtraction in pseudo-C\ estimates. We derive the analytic behaviour of this procedure under the null hypothesis, and use Monte Carlo simulations to investigate its efficiency properties, which appear very promising. For instance, for full sky maps with isotropic white noise the test is able to identify an error of 1% on the noise amplitude estimate.
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Polenta et al. (2005) studied this question.
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