Related papers: Optimal rates for plug-in estimators of density le…
Uniform sampling on implicitly defined manifolds is a core primitive in motion planning, constrained simulation, and probabilistic machine learning. MASEM addresses this problem by entropy-maximizing resampling, but its resampling weights…
We derive optimal rates of convergence in the supremum norm for estimating the H\"older-smooth mean function of a stochastic process which is repeatedly and discretely observed with additional errors at fixed, multivariate, synchronous…
This paper presents minimax rates for density estimation when the data dimension $d$ is allowed to grow with the number of observations $n$ rather than remaining fixed as in previous analyses. We prove a non-asymptotic lower bound which…
The study of minimax convergence rates for classification procedures adapted to SDE paths is rarely addressed in the literature. Only one paper established optimal convergence rates for a binary classifier for SDE paths constructed from the…
Consider the communication-constrained problem of nonparametric function estimation, in which each distributed terminal holds multiple i.i.d. samples. Under certain regularity assumptions, we characterize the minimax optimal rates for all…
We consider the problem of model selection type aggregation in the context of density estimation. We first show that empirical risk minimization is sub-optimal for this problem and it shares this property with the exponential weights…
We introduce the concept of coverage risk as an error measure for density ridge estimation. The coverage risk generalizes the mean integrated square error to set estimation. We propose two risk estimators for the coverage risk and we show…
Given $n$ independent random vectors with common density $f$ on $\mathbb{R}^d$, we study the weak convergence of three empirical-measure based estimators of the convex $\lambda$-level set $L_\lambda$ of $f$, namely the excess mass set, the…
The paper, that continuous some previous work of Sch\"onherr & Schuricht, treats density measures on ${\mathbb R}^n$ that concentrate in any neighborhood of a Lebesgue null set. Such measures are typical for purely finitely additive…
We address the problem of classification when data are collected from two samples with measurement errors. This problem turns to be an inverse problem and requires a specific treatment. In this context, we investigate the minimax rates of…
Let $\rho$ be a general law--invariant convex risk measure, for instance the average value at risk, and let $X$ be a financial loss, that is, a real random variable. In practice, either the true distribution $\mu$ of $X$ is unknown, or the…
We consider the estimation of the global mode of a density under some decay rate condition around the global mode. We show that the maximum of a histogram, with proper choice of bandwidth, achieves the minimax rate that we establish for the…
In classical density (or density-functional) estimation, it is standard to assume that the underlying distribution has a density with respect to the Lebesgue measure. However, when the data distribution is a mixture of continuous and…
Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful…
This paper considers the problem of estimating probabilities of the form $\mathbb{P}(Y \leq w)$, for a given value of $w$, in the situation that a sample of i.i.d.\ observations $X_1, \ldots, X_n$ of $X$ is available, and where we…
Accurate approximation of the sampling distribution of nonparametric kernel density estimators is crucial for many statistical inference problems. Since these estimators have complex asymptotic distributions, bootstrap methods are often…
We construct a kernel density estimator on symmetric spaces of non-compact type and establish an upper bound for its convergence rate, analogous to the minimax rate for classical kernel density estimators on Euclidean space. Symmetric…
Nonparametric density estimation is considered for a discretely observed stationary continuous-time process. For each of three given time sampling procedures either random or deterministic, we establish that histograms and frequency…
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 adaptive minimax estimation of non-linear integral functionals of a density and extend the results obtained for linear and quadratic functionals to general functionals. The typical rate optimal non-adaptive minimax estimators…