Related papers: Rate-optimal and computationally efficient nonpara…

In this paper we study the problem of pointwise density estimation from observations with multiplicative measurement errors. We elucidate the main feature of this problem: the influence of the estimation point on the estimation accuracy. In…

We consider the statistical analysis of data on high-dimensional spheres and shape spaces. The work is of particular relevance to applications where high-dimensional data are available--a commonly encountered situation in many disciplines.…

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…

Obtaining general relations between macroscopic properties of random assemblies, such as density, and the microscopic properties of their constituent particles, such as shape, is a foundational challenge in the study of amorphous materials.…

Recent years have seen an increased interest in the application of methods and techniques commonly associated with machine learning and artificial intelligence to spatial statistics. Here, in a celebration of the ten-year anniversary of the…

We are interested in the problem of robust parametric estimation of a density from $n$ i.i.d. observations. By using a practice-oriented procedure based on robust tests, we build an estimator for which we establish non-asymptotic risk…

New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…

We consider the common problem setting of an elastic sphere impacting on a flexible beam. In contrast to previous studies, we analyze the modal energy distribution induced by the impact, having in mind the particular application of impact…

This paper proposes a new method of bandwidth selection in kernel estimation of density and distribution functions motivated by the connection between maximisation of the entropy of probability integral transforms and maximum likelihood in…

We introduce a novel two-step approach for estimating a probability density function (pdf) given its samples, with the second and important step coming from a geometric formulation. The procedure involves obtaining an initial estimate of…

The estimation of a density profile from experimental data points is a challenging problem, usually tackled by plotting a histogram. Prior assumptions on the nature of the density, from its smoothness to the specification of its form, allow…

Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…

In many statistical and econometric applications, we gather individual samples from various interconnected populations that undeniably exhibit common latent structures. Utilizing a model that incorporates these latent structures for such…

In the study of quantum limits to parameter estimation, the high dimensionality of the density operator and that of the unknown parameters have long been two of the most difficult challenges. Here we propose a theory of quantum…

Kernel estimation of a probability density function supported on the unit interval has proved difficult, because of the well known boundary bias issues a conventional kernel density estimator would necessarily face in this situation.…

We study nonparametric density estimation in non-stationary drift settings. Given a sequence of independent samples taken from a distribution that gradually changes in time, the goal is to compute the best estimate for the current…

Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data…

The paper considers nonparametric kernel density/regression estimation from a stochastic optimization point of view. The estimation problem is represented through a family of stochastic optimization problems. Recursive constrained…

We introduce a fast, high-precision algorithm for calculating intersections between great circle arcs and lines of constant latitude on the unit sphere. We first propose a simplified intersection point formula with improved speed and…

Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical…