Related papers: Exact minimax risk for density estimators in non-i…

This paper continues the research started in \cite{LW16}. In the framework of the convolution structure density model on $\bR^d$, we address the problem of adaptive minimax estimation with $\bL_p$--loss over the scale of anisotropic…

The theory of adaptive estimation and oracle inequalities for the case of Gaussian-shift--finite-interval experiments has made significant progress in recent years. In particular, sharp-minimax adaptive estimators and exact exponential-type…

Nonparametric estimation of nonlocal interaction kernels is crucial in various applications involving interacting particle systems. The inference challenge, situated at the nexus of statistical learning and inverse problems, arises from the…

We derive sufficient conditions for a probability measure on a finite product space (a spin system) to satisfy a (modified) logarithmic Sobolev inequality. We establish these conditions for various examples, such as the (vertex-weighted)…

We estimate on a compact interval densities with isolated irregularities, such as discontinuities or discontinuities in some derivatives. From independent and identically distributed observations we construct a kernel estimator with…

We solve the problem of estimating the distribution of presumed i.i.d. observations for the total variation loss. Our approach is based on density models and is versatile enough to cope with many different ones, including some density…

We provide estimates of the rate of strong approximation and bounds for probabilities of moderate deviations in the CLT for the $L_1$-norm of the kernel density estimator without any assumptions on the density and assuming that the kernel…

Let (V,A) be a weighted graph with a finite vertex set V, with a symmetric matrix of nonnegative weights A and with Laplacian $\Delta$. Let $S_*:V\times V\mapsto{\mathbb{R}}$ be a symmetric kernel defined on the vertex set V. Consider n…

We consider the problem of testing hypotheses on the copula density from $n$ bi-dimensional observations. We wish to test the null hypothesis characterized by a parametric class against a composite nonparametric alternative. Each density…

In this paper, we establish a comprehensive characterization of the generalized Lipschitz classes through the study of the rate of convergence of a family of semi-discrete sampling operators, of Durrmeyer type, in $L^p$-setting. To achieve…

In this paper we study the problem of pointwise density estimation from observations with multiplicative measurement errors. We elucidate the main feature of this problem: the influence of the estimation point on the estimation accuracy. In…

This article is devoted to nonlinear approximation and estimation via piecewise polynomials built on partitions into dyadic rectangles. The approximation rate is studied over possibly inhomogeneous and anisotropic smoothness classes that…

A two-class mixture model, where the density of one of the components is known, is considered. We address the issue of the nonparametric adaptive estimation of the unknown probability density of the second component. We propose a randomly…

We propose a general theorem providing upper bounds for the risk of an empirical risk minimizer (ERM).We essentially focus on the binary classification framework. We extend Tsybakov's analysis of the risk of an ERM under margin type…

We give a new proof of the compactness of minimizing sequences of the Sobolev inequalities in the critical case. Our approach relies on a simplified version of the concentration-compactness principle, which does not require any refinement…

Finite mixture models provide a flexible framework for approximating and estimating multivariate probability densities. We study mixtures formed from translated and rescaled copies of a fixed density kernel and obtain explicit results for…

We prove that kernel density estimation on symmetric spaces of non-compact type, whose L2-risk was bounded above in previous work (Asta,2021), in fact achieves a minimax rate of convergence. With this result, the story for kernel density…

We focus on the nonparametric density estimation problem with directional data. We propose a new rule for bandwidth selection for kernel density estimation. Our procedure is automatic, fully data-driven and adaptive to the smoothness degree…

Within the framework of smoothing spline ANOVA, we propose a plug-in kernel ridge regression estimator to estimate the derivatives of the underlying multivariate regression function. We first establish an $L_\infty$ convergence rate of the…

We consider the minimization problem corresponding to a Sobolev inequality for vector fields and show that minimizing sequences are relatively compact up to the symmetries of the problem. In particular, there is a minimizer. An ingredient…