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Accurate calculations of the spectral density in a strongly correlated quantum many-body system are of fundamental importance to study its dynamics in the linear response regime. Typical examples are the calculation of inclusive and…
Density estimation is a fundamental technique employed in various fields to model and to understand the underlying distribution of data. The primary objective of density estimation is to estimate the probability density function of a random…
We study dense packings of a large number of congruent non-overlapping circles inside a square by looking for configurations which maximize the packing density, defined as the ratio between the area occupied by the disks and the area of the…
Density estimation is an important technique for characterizing distributions given observations. Much existing research on density estimation has focused on cases wherein the data lies in a Euclidean space. However, some kinds of data are…
Spherical radial-basis-based kernel interpolation abounds in image sciences including geophysical image reconstruction, climate trends description and image rendering due to its excellent spatial localization property and perfect…
Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…
We study mapping properties of operators with kernels defined via a combination of continuous and discrete orthogonal polynomials, which provide an abstract formulation of quantum (q-) Fourier type systems. We prove Ismail conjecture…
Within the framework of hierarchical clustering we show that a simple Press-Schechter-like approximation, based on spherical dynamics, provides a good estimate of the evolution of the density field in the quasi-linear regime up to $\Sigma…
Dimensionality reduction is a crucial technique in data analysis, as it allows for the efficient visualization and understanding of high-dimensional datasets. The circular coordinate is one of the topological data analysis techniques…
Density estimation plays a fundamental role in many areas of statistics and machine learning. Parametric, nonparametric and semiparametric density estimation methods have been proposed in the literature. Semiparametric density models are…
Nonparametric density estimation is of great importance when econometricians want to model the probabilistic or stochastic structure of a data set. This comprehensive review summarizes the most important theoretical aspects of kernel…
A nonparametric kernel density estimator for directional-linear data is introduced. The proposal is based on a product kernel accounting for the different nature of both (directional and linear) components of the random vector. Expressions…
We are interested in the rate of consistency of kernel density estimators with respect to the weighted sup-norm determined by some unbounded weight function. This problem has been considered by Gine, Koltchinskii and Zinn (2004) for a…
We show that rate-adaptive multivariate density estimation can be performed using Bayesian methods based on Dirichlet mixtures of normal kernels with a prior distribution on the kernel's covariance matrix parameter. We derive sufficient…
We introduce \emph{topological density estimation} (TDE), in which the multimodal structure of a probability density function is topologically inferred and subsequently used to perform bandwidth selection for kernel density estimation. We…
A modified gamma kernel should not be automatically preferred to the standard gamma kernel, especially for univariate convex densities with a pole at the origin. In the multivariate case, multiple combined gamma kernels, defined as a…
We show that the cumulative distribution function corresponding to a kernel density estimator with optimal bandwidth lies outside any confidence interval, around the empirical distribution function, with probability tending to 1 as the…
In classical density (or density-functional) estimation, it is standard to assume that the underlying distribution has a density with respect to the Lebesgue measure. However, when the data distribution is a mixture of continuous and…
A novel nonparametric clustering algorithm is proposed using the interpoint distances between the members of the data to reveal the inherent clustering structure existing in the given set of data, where we apply the classical nonparametric…
Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…