Related papers: Optimal Quantization for Nonuniform Densities on S…
This paper studies density estimation and regression analysis with contaminated data observed on the unit hypersphere S^d. Our methodology and theory are based on harmonic analysis on general S^d. We establish novel nonparametric density…
We construct optimal measurements, achieving the ultimate precision predicted by quantum theory, for the simultaneous estimation of centroid, separation, and relative intensities of two incoherent point sources using a linear optical…
Finding the optimal random packing of non-spherical particles is an open problem with great significance in a broad range of scientific and engineering fields. So far, this search has been performed only empirically on a case-by-case basis,…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…
The representation of a given quantity with less information is often referred to as `quantization' and it is an important subject in information theory. In this paper, we have considered absolutely continuous probability measures on unit…
Conjunction assessment requires knowledge of the uncertainty in the predicted orbit. Errors in the atmospheric density are a major source of error in the prediction of low Earth orbits. Therefore, accurate estimation of the density and…
The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability…
Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. In this paper, we have considered a Borel probability measure…
We consider a process given as the solution of a stochastic differential equation with irregular, path dependent and time-inhomogeneous drift coefficient and additive noise. Explicit and optimal bounds for the Lebesgue density of that…
In this paper, we will discuss how to generalize nonparametric density estimators to MLE parametric estimators. Basing on the Parzen window theory and using the advantages of probability amplitude of quantum theory, we model a nonlinear…
We analyze the convergence of probability density functions utilizing approximate models for both forward and inverse problems. We consider the standard forward uncertainty quantification problem where an assumed probability density on…
We formulate an optimization problem to estimate probability densities in the context of multidimensional problems that are sampled with uneven probability. It considers detector sensitivity as an heterogeneous density and takes advantage…
Probability mass curves the data space with horizons. Let f be a multivariate probability density function with continuous second order partial derivatives. Consider the problem of estimating the true value of f(z) > 0 at a single point z,…
Probability density estimation is a core problem of statistics and signal processing. Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severely…
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.…
This paper considers statistical estimation problems where the probability distribution of the observed random variable is invariant with respect to actions of a finite topological group. It is shown that any such distribution must satisfy…
We consider nonparametric estimation of the derivative of a probability density function with the bounded support on $[0,\infty)$. Estimates are looked up in the class of estimates with asymmetric gamma kernel functions. The use of gamma…
Entropic uncertainty relations play a fundamental role in quantum information theory. However, determining optimal (tight) entropic uncertainty relations for general observables remains a formidable challenge and has so far been achieved…
The number of times that we can access a system to extract information via quantum metrology is always finite, and possibly small, and realistic amounts of prior knowledge tend to be moderate. Thus theoretical consistency demands a…
Complex signal detection in additive noise can be performed by a one-sample bivariate location test. Spherical symmetry is assumed for the noise density as well as closedness with respect to linear transformation. Therefore the noise is…