Related papers: Adaptive Density Estimation on Bounded Domains
There is an intense and partly recent literature focussing on the problem of selecting the bandwidth parameter for kernel density estimators. Available methods are largely `very nonparametric', in the sense of not requiring any knowledge…
We consider non-parametric estimation problems in the presence of dependent data, notably non-parametric regression with random design and non-parametric density estimation. The proposed estimation procedure is based on a dimension…
New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of depen\-dence of design elements. The estimators are the…
We are studying the problem of estimating density in a wide range of metric spaces, including the Euclidean space, the sphere, the ball, and various Riemannian manifolds. Our framework involves a metric space with a doubling measure and a…
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 introduce a robust and fully adaptive method for pointwise estimation in heteroscedastic regression. We allow for noise and design distributions that are unknown and fulfill very weak assumptions only. In particular, we do not impose…
We study the performances of an adaptive procedure based on a convex combination, with data-driven weights, of term-by-term thresholded wavelet estimators. For the bounded regression model, with random uniform design, and the nonparametric…
The rate of normal approximation for the integral norm of kernel density estimators is investigated in the case of densities with power-type singularities. The quantities from the formulations of published results by the author are…
In the present paper, we consider the estimation of a periodic two-dimensional function $f(\cdot,\cdot)$ based on observations from its noisy convolution, and convolution kernel $g(\cdot,\cdot)$ unknown. We derive the minimax lower bounds…
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…
The performance of kernel density estimators is usually studied via Taylor expansions and asymptotic approximation arguments, in which the bandwidth parameter tends to zero with increasing sample size. In contrast, this paper focusses…
Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…
The purpose of this paper is to estimate the intensity of a Poisson process $N$ by using thresholding rules. In this paper, the intensity, defined as the derivative of the mean measure of $N$ with respect to $ndx$ where $n$ is a fixed…
This work proposes a framework LGKDE that learns kernel density estimation for graphs. The key challenge in graph density estimation lies in effectively capturing both structural patterns and semantic variations while maintaining…
This paper investigates the nonparametric estimation of a heteroskedastic variance function on the sphere in a regression framework, assuming the variance belongs to a Besov regularity class. A needlet-based estimator is proposed, combining…
We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion…
In the context of density level set estimation, we study the convergence of general plug-in methods under two main assumptions on the density for a given level $\lambda$. More precisely, it is assumed that the density (i) is smooth in a…
In this paper we prove large and moderate deviations principles for the recursive kernel estimators of a probability density function defined by the stochastic approximation algorithm introduced by Mokkadem et al. [2009. The stochastic…
We present a new non-parametric estimator of the conditional density of the kernel type. It is based on an efficient transformation of the data by quantile transform. By use of the copula representation, it turns out to have a remarkable…
Given an i.i.d. sample drawn from a density $f$, we propose to test that $f$ equals some prescribed density $f_0$ or that $f$ belongs to some translation/scale family. We introduce a multiple testing procedure based on an estimation of the…