Related papers: A maximum volume density estimator generalized ove…
We derive a scale-free bound on the density of the maximum of a centered Gaussian vector. The basic bound is non-uniform, depends logarithmically on the dimension, and allows any covariance matrix. When the largest marginal variance is…
(abridged) We present a new determination of the local temperature function of X-ray clusters. We use a new sample comprising fifty clusters for which temperature information is now available, making it the largest complete sample of its…
Capture-recapture methods aim to estimate the size of a closed population on the basis of multiple incomplete enumerations of individuals. In many applications, the individual probability of being recorded is heterogeneous in the…
When extracting the weak lensing shear signal, one may employ either locally normalized or globally normalized shear estimators. The former is the standard approach when estimating cluster masses, while the latter is the more common method…
Estimating the density of a distribution from samples is a fundamental problem in statistics. In many practical settings, the Wasserstein distance is an appropriate error metric for density estimation. For example, when estimating…
Cosmic Microwave Background (CMB) lensing is a powerful probe of the matter distribution in the Universe. The standard quadratic estimator, which is typically used to measure the lensing signal, is known to be suboptimal for low-noise…
An excess up-scattering mass bias on a weak lensing cluster mass estimate is a statistical bias that an observed weak lensing mass ($M_{\rm obs}$) of a cluster of galaxies is, in a statistical sense, larger than its true mass ($M_{\rm…
Estimating the density of a continuous random variable X has been studied extensively in statistics, in the setting where n independent observations of X are given a priori and one wishes to estimate the density from that. Popular methods…
We prove a harmonic asymptotics density theorem for asymptotically flat initial data sets with compact boundary that satisfy the dominant energy condition. We use this to settle the spacetime positive mass theorem, with rigidity, for…
One key issue in several astrophysical problems is the evaluation of the density probability function underlying an observational discrete data set. We here review two non-parametric density estimators which recently appeared in the…
We investigate density estimation from a $n$-sample in the Euclidean space $\mathbb R^D$, when the data is supported by an unknown submanifold $M$ of possibly unknown dimension $d < D$ under a reach condition. We study nonparametric kernel…
Forthcoming large-scale spectroscopic surveys will soon provide data on thousands of galaxy clusters. It is important that the systematics of the various mass estimation techniques are well understood and calibrated. We compare three…
We introduce the tracer mass estimator. This is a new and simple way to estimate the enclosed mass from the projected positions and line of sight velocities of a tracer population (such as globular clusters, halo stars and planetary…
Density ratio estimation serves as an important technique in the unsupervised machine learning toolbox. However, such ratios are difficult to estimate for complex, high-dimensional data, particularly when the densities of interest are…
We present a universal technique for quantum state estimation based on the maximum-likelihood method. This approach provides a positive definite estimate for the density matrix from a sequence of measurements performed on identically…
We propose a new wavelet-based method for density estimation when the data are size-biased. More specifically, we consider a power of the density of interest, where this power exceeds 1/2. Warped wavelet bases are employed, where warping is…
The histogram method is a powerful non-parametric approach for estimating the probability density function of a continuous variable. But the construction of a histogram, compared to the parametric approaches, demands a large number of…
Truncated densities are probability density functions defined on truncated domains. They share the same parametric form with their non-truncated counterparts up to a normalizing constant. Since the computation of their normalizing constants…
The traditional kernel density estimator of an unknown density is by construction completely nonparametric, in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of…
We present constraints on the mean matter density, Omega_m, the normalization of the density fluctuation power spectrum, sigma_8, and the dark-energy equation-of-state parameter, w, obtained from measurements of the X-ray luminosity…