Related papers: A maximum volume density estimator generalized ove…
This is the fourth in a series of papers studying the astrophysics and cosmology of massive, dynamically relaxed galaxy clusters. Here, we use measurements of weak gravitational lensing from the Weighing the Giants project to calibrate…
Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges…
We present in this article an analysis of some of the properties of the density field realized in numerical simulations for power-law initial power-spectra in the case of a critical density universe. We compare our numerical results in the…
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…
We investigate Bayesian nonparametric density estimation via orthogonal polynomial expansions in weighted Sobolev spaces. A core challenge is establishing minimax optimal posterior convergence rates, especially for densities on unbounded…
We examine the systematics affecting the X-ray mass estimators applied to a set of five simulated galaxy clusters. They have been processed through the X-ray Map Simulator, X-MAS, to provide Chandra-like long exposures that are analyzed to…
Assume that we observe i.i.d.~points lying close to some unknown $d$-dimensional $\mathcal{C}^k$ submanifold $M$ in a possibly high-dimensional space. We study the problem of reconstructing the probability distribution generating the…
A new X-ray selected and X-ray flux-limited galaxy cluster sample is presented. Based on the ROSAT All-Sky Survey the 63 brightest clusters with galactic latitude |bII| >= 20 deg and flux fx(0.1-2.4 keV) >= 2 * 10^{-11} ergs/s/cm^2 have…
Symplectic integrators are widely used for the study of planetary dynamics and other $N$-body problems. In a study of the outer Solar system, we demonstrate that individual symplectic integrations can yield biased errors in the semi-major…
Using data from 289 numerical relativity simulations of merging binary neutron stars, we identify, for the first time, a robust quasi-universal relation connecting the postmerger peak gravitational-wave frequency and the value of the…
We use cosmological gas dynamic simulations to investigate the accuracy of galaxy cluster mass estimates based on X-ray observations. The experiments follow the formation of clusters in different cosmological models and include the effects…
Density functions that represent sample data are often multimodal, i.e. they exhibit more than one maximum. Typically this behavior is taken to indicate that the underlying data deserves a more detailed representation as a mixture of…
It is well known that, under standard regularity conditions, the maximum likelihood estimator (MLE) satisfies a central limit theorem and converges in distribution to a Gaussian random variable as the sample size grows. This paper…
We demonstrate that the maximum-entropy method for gravitational lens reconstruction presented in Bridle et al. (1998) may be applied even when only shear \emph{or} magnification information is present. We also demonstrate that the method…
This paper proposes a novel method for testing observability in Gaussian models using discrete density approximations (deterministic samples) of (multivariate) Gaussians. Our notion of observability is defined by the existence of the…
We provide an abstract multivariate central limit theorem with the Lindeberg-type error bounded in terms of Lipschitz functions (Wasserstein 1-distance) or functions with bounded second or third derivatives. The result is proved by means of…
This paper focuses on the problem of unbounded density ratio estimation -- an understudied yet critical challenge in statistical learning -- and its application to covariate shift adaptation. Much of the existing literature assumes that the…
In this paper we address smoothing-that is, optimisation-based-estimation techniques for localisation problems in the case where motion sensors are very accurate. Our mathematical analysis focuses on the difficult limit case where motion…
A bias-reduced estimator is proposed for the mean absolute deviation parameter of a median regression model. A workaround is devised for the lack of smoothness in the sense conventionally required in general bias-reduced estimation. A local…
The general regularisation scheme, a versatile approach for nonparametric estimation, has been successfully applied to regression, density ratio, and score estimation. In this paper, we introduce a unified framework encompassing these…