Unbiased Estimation of an Angular Power Spectrum

Abstract

We discuss the derivation of 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 for testing for the presence of residual bias due to inappropriate noise subtraction in pseudo-$C_{\ell }$ estimates. We derive the analytic behavior 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.

replaced with version published in JCAP. Added discussion about polarization measurements and 1/f noise correlated among different detectors

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• Measurements of the E-Mode Polarization and Temperature-E-Mode Correlation of the CMB from SPT-3G 2018 Data
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• A measurement of secondary cosmic microwave background anisotropies from the 2500-square-degree SPT-SZ survey
• Measurements of the Temperature and E-Mode Polarization of the CMB from 500 Square Degrees of SPTpol Data
• Measurements of Secondary Cosmic Microwave Background Anisotropies with the South Pole Telescope
• Angular Power Spectra of the Millimeter Wavelength Background Light from Dusty Star-forming Galaxies with the South Pole Telescope
• Measurements of Sub-degree B-mode Polarization in the Cosmic Microwave Background from 100 Square Degrees of SPTpol Data
• An Improved Measurement of the Secondary Cosmic Microwave Background Anisotropies from the SPT-SZ + SPTpol Surveys
• Planck 2018 results. II. Low Frequency Instrument data processing
• Planck 2013 results. II. Low Frequency Instrument data processing
• Improved constraints on cosmic microwave background secondary anisotropies from the complete 2008 South Pole Telescope data
• Polarized CMB power spectrum estimation using the pure pseudo-cross-spectrum approach
• CMB Polarization B-mode Delensing with SPTpol and Herschel
• Planck 2015 results. II. Low Frequency Instrument data processing
• CMB power spectrum estimation using wavelets
• Measurements of E-Mode Polarization and Temperature-E-Mode Correlation in the Cosmic Microwave Background from 100 Square Degrees of SPTpol Data
• Low Variance at large scales of WMAP 9 year data
• New estimates of the CMB angular power spectra from the WMAP 5 yrs low resolution data
• Planck 2018 constraints on anisotropic birefringence and its cross-correlation with CMB anisotropy
• SZE Signals in Cluster Models
• Statistical challenges in the analysis of Cosmic Microwave Background radiation
• Methods for pixel domain correction of EB leakage
• Planck intermediate results. XLIX. Parity-violation constraints from polarization data
• Multi-Clustering Needlet-ILC for CMB B-modes component separation
• A comparison of CMB Angular Power Spectrum Estimators at Large Scales: the TT case
• Non-Gaussian Scatter in Cluster Scaling Relations
• Ergodicity and Gaussianity for Spherical Random Fields
• Stacking weak lensing signals of SZ clusters to constrain cluster physics
• Optimization of foreground moment deprojection for semi-blind CMB polarization reconstruction
• Correlated Component Analysis for diffuse component separation with error estimation on simulated Planck polarization data
• Consistency of cosmic microwave background temperature measurements in three frequency bands in the 2500-square-degree SPT-SZ survey
• Measurements of the Cross Spectra of the Cosmic Infrared and Microwave Backgrounds from 95 to 1200 GHz
• Using CMB data to constrain non-isotropic Planck-scale modifications to Electrodynamics
• LiteBIRD Science Goals and Forecasts: Primordial Magnetic Fields
• A cross-correlation analysis of CMB lensing and radio galaxy maps
• Fundamental Plane of Sunyaev-Zeldovich clusters
• The Atacama Cosmology Telescope: Semi-Analytic Covariance Matrices for the DR6 CMB Power Spectra
• Gaussian semiparametric estimates on the unit sphere
• On the effect of cosmic rays in bolometric CMB measurements from the stratosphere
• Detectability of Galactic Faraday Rotation in Multi-wavelength CMB Observations: A Cross-Correlation Analysis of CMB and Radio Maps