Related papers: Theoretical Analysis of Nonparametric Filament Est…

One key issue in several astrophysical problems is the evaluation of the density probability function underlying an observational discrete data set. We here review two non-parametric density estimators which recently appeared in the…

In this paper, we consider the distribution of the supremum of non-stationary Gaussian processes, and present a new theoretical result on the asymptotic behaviour of this distribution. Unlike previously known facts in this field, our main…

A stationary Gaussian process is said to be long-range dependent (resp., anti-persistent) if its spectral density $f(\lambda)$ can be written as $f(\lambda)=|\lambda|^{-2d}g(|\lambda|)$, where $0<d<1/2$ (resp., $-1/2<d<0$), and $g$ is…

The paper considers probability distribution, density, conditional distribution and density and conditional moments as well as their kernel estimators in spaces of generalized functions. This approach does not require restrictions on…

We consider kernel estimation of marginal densities and regression functions of stationary processes. It is shown that for a wide class of time series, with proper centering and scaling, the maximum deviations of kernel density and…

Surface integrals on density level sets often appear in asymptotic results in nonparametric level set estimation (such as for confidence regions and bandwidth selection). Also surface integrals can be used to describe the shape of level…

We provide new asymptotic theory for kernel density estimators, when these are applied to autoregressive processes exhibiting moderate deviations from a unit root. This fills a gap in the existing literature, which has to date considered…

Consider the problem when $X_1,X_2,..., X_n$ are distributed on a circle following an unknown distribution $F$ on $S^1$. In this article we have consider the absolute general set-up where the density can have local features such as…

Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…

We consider approximate maximum likelihood parameter estimation in nonlinear state-space models. We discuss both direct optimization of the likelihood and expectation--maximization (EM). For EM, we also give closed-form expressions for the…

Mixture models are regularly used in density estimation applications, but the problem of estimating the mixing distribution remains a challenge. Nonparametric maximum likelihood produce estimates of the mixing distribution that are…

We study the problem of the non-parametric estimation for the density $\pi$ of the stationary distribution of a stochastic two-dimensional damping Hamiltonian system $(Z_t)_{t\in[0,T]}=(X_t,Y_t)_{t \in [0,T]}$. From the continuous…

Parametric density estimation, for example as Gaussian distribution, is the base of the field of statistics. Machine learning requires inexpensive estimation of much more complex densities, and the basic approach is relatively costly…

Indirect inference estimators (i.e., simulation-based minimum distance estimators) in a parametric model that are based on auxiliary non-parametric maximum likelihood density estimators are shown to be asymptotically normal. If the…

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…

The extraction of filamentary structure from a point cloud is discussed. The filaments are modeled as ridge lines or higher dimensional ridges of an underlying density. We propose two novel algorithms, and provide theoretical guarantees for…

This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior…

We propose a novel approach for density estimation called histogram trend filtering. Our estimator arises from looking at surrogate Poisson model for counts of observations in a partition of the support of the data. We begin by showing…

Recent work has focused on the problem of nonparametric estimation of information divergence functionals. Many existing approaches are restrictive in their assumptions on the density support set or require difficult calculations at the…

In this paper we study nonparametric estimators of copulas and copula densities. We first focus our study on a density copula estimator based on a polynomial orthogonal projection of the joint density. A new copula estimator is then…