Related papers: Shrinking the Quadratic Estimator
In a previous article, a least square regression estimation procedure was proposed: first, we condiser a family of functions and study the properties of an estimator in every unidimensionnal model defined by one of these functions; we then…
We propose an estimator defined in real space for the reconstruction of the weak lensing potential due to the intervening large scale structure from high resolution maps of the cosmic microwave background. This estimator was motivated as an…
The study of the Cosmic Microwave Background (CMB) lensing potential has established itself by now as a robust way of probing the physics of large-scale structure growth. The most common estimators of the lensing potential are derived under…
Galaxy-galaxy weak lensing provides a powerful means of measuring the average matter distribution around lens galaxies -- i.e., the galaxy bias relation. Properly accounting for the spin-2 nature of weak lensing distortions, we develop a…
In this paper, we study the problem of adaptive estimation of the spectral density of a stationary Gaussian process. For this purpose, we consider a wavelet-based method which combines the ideas of wavelet approximation and estimation by…
Weak lensing measurements are starting to provide statistical maps of the distribution of matter in the universe that are increasingly precise and complementary to cosmic microwave background maps. The probability distribution (PDF)…
Precise reconstruction of the cosmic microwave background lensing potential can be achieved with deep polarization surveys by iteratively removing lensing-induced $B$ modes. We introduce a lensing spectrum estimator and its likelihood for…
Weak gravitational lensing by intervening large-scale structure induces a distinct signature in the cosmic microwave background (CMB) that can be used to reconstruct the weak-lensing displacement map. Estimators for individual Fourier modes…
In recent years, weak lensing of the cosmic microwave background (CMB) has emerged as a powerful tool to probe fundamental physics, such as neutrino masses, primordial non-Gaussianity, dark energy, and modified gravity. The prime target of…
The three cardinal, statistically consistent, families of non-parametric estimators to the power spectral density of a time series are lag-window, multitaper and Welch estimators. However, when estimating power spectral densities from a…
In this paper, we attempt to shed light on a new class of nonstationary random fields which exhibit, what we call, local invariant nonstationarity. We argue that the local invariant property has a special interaction with a new generalized…
In the very near future, weak lensing surveys will map the projected density of the universe in an unbiased way over large regions of the sky. In order to interpret the results of studies it is helpful to develop an understanding of the…
This paper deals with the robust estimation problem of a signal given noisy observations. We assume that the actual statistics of the signal and observations belong to a ball about the nominal statistics. This ball is formed by placing a…
In paper I (Yu et al. [1]), we show through N-body simulation that a local monotonic Gaussian transformation can significantly reduce non-Gaussianity in a noise-free lensing convergence field. This makes the Gaussianization a promising…
Large catalogs of shear-selected peaks have recently become a reality. In order to properly interpret the abundance and properties of these peaks, it is necessary to take into account the effects of the clustering of source galaxies, among…
The formalism of Wiener filtering is developed here for the purpose of reconstructing the large scale structure of the universe from noisy, sparse and incomplete data. The method is based on a linear minimum variance solution, given data…
We study the performance of estimators of a sparse nonrandom vector based on an observation which is linearly transformed and corrupted by additive white Gaussian noise. Using the reproducing kernel Hilbert space framework, we derive a new…
Large-scale Fourier modes of the cosmic density field are of great value for learning about cosmology because of their well-understood relationship to fluctuations in the early universe. However, cosmic variance generally limits the…
Detecting anisotropic screening of the cosmic microwave background (CMB) holds the promise of revealing the distribution of gas in the Universe, characterizing the complex processes of galaxy formation and feedback, and studying the epoch…
We consider statistical models where functional data are artificially contaminated by independent Wiener processes in order to satisfy privacy constraints. We show that the corrupted observations have a Wiener density which determines the…