Scalar quadratic maximum likelihood estimators for the CMB cross power spectrum

Understand

Estimating the cross-correlation power spectra of cosmic microwave background (CMB), in particular, the T B and EB spectra, is important for testing parity symmetry in cosmology and diagnosing insidious instruments systematics.

• The Quadratic Maximum Likelihood (QML) estimator provides the optimal estimates of power spectra, but it is computationally very expensive.
• The hybrid pseudo-Cl estimator is computationally fast but performs poorly on large scales.
• As a natural extension of previous work (Chen et al.