Related papers: On the density of nonlinear statistics
We show a statistical version of Taylor's theorem and apply this result to non-parametric density estimation from truncated samples, which is a classical challenge in Statistics \cite{woodroofe1985estimating, stute1993almost}. The…
We consider the problem of estimating the density of observations taking values in classical or nonclassical spaces such as manifolds and more general metric spaces. Our setting is quite general but also sufficiently rich in allowing the…
This note examines the infinite divisibility of density-based transformations of normal random variables. We characterize a class of density-based transformations of normal variables which produces non-infinitely divisible distributions. We…
We prove the existence, uniqueness and non negativity of solutions for a nonlinear stationary Doi-Edwards equation. The existence is proved by a perturbation argument. We get the uniqueness and the non negativity by showing the convergence…
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 discuss some old results due to Abel and Olivier concerning the convergence of positive series and prove a set of necessary conditions involving convergence in density.
Various problems in Engineering and Statistics require the computation of the likelihood ratio function of two probability densities. In classical approaches the two densities are assumed known or to belong to some known parametric family.…
In quantum optics, measurement statistics -- for example, photocounting statistics -- are considered nonclassical if they cannot be reproduced with statistical mixtures of classical radiation fields. We have formulated a necessary and…
The notion of density of a finite set is discussed. We proof a general theorem of set theory which refines Bose-Einstein distribution.
The paper solves the problems of determining the asymptotics of the number of primes and the sums of functions of primes in a subset of the natural series that satisfies the conditions that the asymptotic density of the number of primes in…
We undertake a systematic review of some results concerning local well-posedness of the Cauchy problem for certain systems of nonlinear wave equations, with minimal regularity assumptions on the initial data. Moreover we provide a…
We propose a new model for nonstationary integer-valued time series which is particularly suitable for data with a strong trend. In contrast to popular Poisson-INGARCH models, but in line with classical GARCH models, we propose to pick the…
In this paper we consider the isoperimetric problem with double density in an Euclidean space, that is, we study the minimisation of the perimeter among subsets of $\mathbb{R}^n$ with fixed volume, where volume and perimeter are relative to…
We present a new topological proof of the infinitude of prime numbers with a new topology. Furthermore, in this topology, we characterize the infinitude of any non-empty subset of prime numbers.
The concept of biased data is well known and its practical applications range from social sciences and biology to economics and quality control. These observations arise when a sampling procedure chooses an observation with probability that…
We shall study special regularity properties of solutions to some nonlinear dispersive models. The goal is to show how regularity on the initial data is transferred to the solutions. This will depend on the spaces where regularity is…
Necessary and sufficient conditions of uniform consistency are explored. A hypothesis is simple. Nonparametric sets of alternatives are bounded convex sets in $\mathbb{L}_p$, $p >1$ with "small" balls deleted. The "small" balls have the…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…
We introduce a probabilistic representation for solutions of quasilinear wave equation with analytic nonlinearities. We use stochastic cascades to prove existence and uniqueness of the solution.
The problem of separating structured information representing phenomena of differing natures is considered. A structure is assumed to be independent of the others if can be represented in a complementary subspace. When the concomitant…