Related papers: A note on extreme values and kernel estimators of …
In this paper we propose a new method of joint nonparametric estimation of probability density and its support. As is well known, nonparametric kernel density estimator has "boundary bias problem" when the support of the population density…
This work studies the problem of estimating a two-dimensional superposition of point sources or spikes from samples of their convolution with a Gaussian kernel. Our results show that minimizing a continuous counterpart of the $\ell_1$ norm…
Define the scaled empirical point process on an independent and identically distributed sequence $\{Y_i: i\le n\}$ as the random point measure with masses at $a_n^{-1} Y_i$. For suitable $a_n$ we obtain the weak limit of these point…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
Given a statistical model, we propose a novel estimation method that yields randomised estimators for the unknown distribution of an observed random variable. We establish non-asymptotic bounds for the performance of these estimators and…
We investigate random graphs on the points of a Poisson process in $d$-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point carries an independent random mark and given marks and…
Given a sample from a discretely observed compound Poisson process, we consider estimation of the density of the jump sizes. We propose a kernel type nonparametric density estimator and study its asymptotic properties. An order bound for…
We consider stationary configurations of points in Euclidean space which are marked by positive random variables called scores. The scores are allowed to depend on the relative positions of other points and outside sources of randomness.…
This paper addresses the problem of learning the impulse responses characterizing forward models by means of a regularized kernel-based Prediction Error Method (PEM). The common approach to accomplish that is to approximate the system with…
We give a characterization of the invariant measures for the exclusion process on the integers with certain reversible transition kernels. Some examples include all nearest-neighbor kernels with asymptotic mean zero. One tool used is a…
We continue here the study of free extreme values begun in Ben Arous and Voiculescu (2006). We study the convergence of the free point processes associated with free extreme values to a free Poisson random measure (Voiculescu (1998),…
The notion of a (polynomial) kernelization from parameterized complexity is a well-studied model for efficient preprocessing for hard computational problems. By now, it is quite well understood which parameterized problems do or…
This paper considers the finite element solution of the boundary value problem of Poisson's equation and proposes a guaranteed em a posteriori local error estimation based on the hypercircle method. Compared to the existing literature on…
Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which…
Density estimation is a crucial component of many machine learning methods, and manifold learning in particular, where geometry is to be constructed from data alone. A significant practical limitation of the current density estimation…
In this paper, a kernel estimator of the differential entropy of the mark distribution of a homogeneous Poisson marked point process is proposed. The marks have an absolutely continuous distribution on a compact Riemannian manifold without…
We present a solution to a problem suggested by Philippe Biane: We prove that a certain Plancherel-type probability distribution on partitions converges, as partitions get large, to a new determinantal random point process on the set…
We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or equivalently, the value of a linear programming problem with…
We study limiting properties of ratios of ordered points of point processes whose intensity measures have regularly varying tails, giving a systematic treatment which points the way to "large-trimming" properties of extremal processes and a…
In this paper, we develop a computational approach for estimating the mean value of a quantity in the presence of uncertainty. We demonstrate that, under some mild assumptions, the upper and lower bounds of the mean value are efficiently…