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We extend balloon and sample-smoothing estimators, two types of variable-bandwidth kernel density estimators, by a shift parameter and derive their asymptotic properties. Our approach facilitates the unified study of a wide range of density…
Communication-enabled devices routinely carried by individuals have become pervasive, opening unprecedented opportunities for collecting digital metadata about the mobility of large populations. In this paper, we propose a novel methodology…
We consider estimation of the common probability density $f$ of i.i.d. random variables $X_i$ that are observed with an additive i.i.d. noise. We assume that the unknown density $f$ belongs to a class $\mathcal{A}$ of densities whose…
We consider a nonparametric Bayesian approach to estimation and testing for a multivariate monotone density. Instead of following the conventional Bayesian route of putting a prior distribution complying with the monotonicity restriction,…
The magnification of distant sources by mass clumps at lower ($z \leq 1$) redshifts is calculated analytically. The clumps are initially assumed to be galaxy group isothermal spheres with properties inferred from an extensive survey. The…
We propose a novel approach for density estimation called histogram trend filtering. Our estimator arises from looking at surrogate Poisson model for counts of observations in a partition of the support of the data. We begin by showing…
Analytic continuation of imaginary time or frequency data to the real axis is a crucial step in extracting dynamical properties from quantum Monte Carlo simulations. The average spectrum method provides an elegant solution by integrating…
Volumetry is one of the principal downstream applications of 3D medical image segmentation, for example, to detect abnormal tissue growth or for surgery planning. Conformal Prediction is a promising framework for uncertainty quantification,…
Real-world measurements often comprise a dominant signal contaminated by a noisy background. Robustly estimating the dominant signal in practice has been a fundamental statistical problem. Classically, mixture models have been used to…
The performance of kernel density estimators is usually studied via Taylor expansions and asymptotic approximation arguments, in which the bandwidth parameter tends to zero with increasing sample size. In contrast, this paper focusses…
Selection of galaxy clusters by mass is now possible due to weak gravitational lensing effects. It is an important question then whether this type of selection reduces the projection effects prevalent in optically selected cluster samples.…
We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics and machine learning. We give the first minimax-optimal rates…
We consider the problem of Bayesian density estimation on the positive semiline for possibly unbounded densities. We propose a hierarchical Bayesian estimator based on the gamma mixture prior which can be viewed as a location mixture. We…
We present a new method for estimating galaxy cluster masses using weak-lensing magnification. The effect of weak-lensing magnification introduces a correlation between the position of foreground galaxy clusters and the density of…
Density estimation for geospatial data ideally relies on precise geocoordinates, typically defined by longitude and latitude. However, such detailed information is often unavailable due to confidentiality constraints. As a result, analysts…
Statistical inference based on optimal transport offers a different perspective from that of maximum likelihood, and has increasingly gained attention in recent years. In this paper, we study univariate nonparametric shape-constrained…
Accurate density estimation methodologies play an integral role in a variety of scientific disciplines, with applications including simulation models, decision support tools, and exploratory data analysis. In the past, histograms and kernel…
Grouped data are commonly encountered in applications. The Bernstein polynomial model is proposed as an approximate model in this paper for estimating a univariate density function based on grouped data. The coefficients of the Bernstein…
We use a self-consistent modeling of x-ray cluster properties to constrain cosmological scenarios of structure formation in the case of open cosmological models. We first show that an unbiased open model can reproduce present day…
Concentration inequalities for the sample mean, like those due to Bernstein, Hoeffding, and Bentkus, are valid for any sample size but overly conservative, yielding confidence intervals that are unnecessarily wide. The central limit theorem…