Shrinking the Quadratic Estimator

Abstract

We study a regression characterization for the quadratic estimator of weak lensing, developed by Hu and Okamoto (2001,2002), for cosmic microwave background observations. This characterization motivates a modification of the quadratic estimator by an adaptive Wiener filter which uses the robust Bayesian techniques described in Strawderman (1971) and Berger (1980). This technique requires the user to propose a fiducial model for the spectral density of the unknown lensing potential but the resulting estimator is developed to be robust to misspecification of this model. The role of the fiducial spectral density is to give the estimator superior statistical performance in a "neighborhood of the fiducial model" while controlling the statistical errors when the fiducial spectral density is drastically wrong. Our estimate also highlights some advantages provided by a Bayesian analysis of the quadratic estimator.

References in corpus (6)

• Detection of the Power Spectrum of Cosmic Microwave Background Lensing by the Atacama Cosmology Telescope
• Evidence for dark energy from the cosmic microwave background alone using the Atacama Cosmology Telescope lensing measurements
• CMB temperature lensing power reconstruction
• Cosmological Information from Lensed CMB Power Spectra
• Real space estimator for the weak lensing convergence from the CMB
• Mapping gravitational lensing of the CMB using local likelihoods