Related papers: Optimal rates for plug-in estimators of density le…

In this paper we develop rate--optimal estimation procedures in the problem of estimating the $L_p$--norm, $p\in (0, \infty)$ of a probability density from independent observations. The density is assumed to be defined on $R^d$, $d\geq 1$…

We study the convergence properties, in Hellinger and related distances, of nonparametric density estimators based on measure transport. These estimators represent the measure of interest as the pushforward of a chosen reference…

Estimating the ratio of two probability densities from finitely many observations of the densities is a central problem in machine learning and statistics with applications in two-sample testing, divergence estimation, generative modeling,…

Divergence estimators based on direct approximation of density-ratios without going through separate approximation of numerator and denominator densities have been successfully applied to machine learning tasks that involve distribution…

We analyze the $\ell_1$ and $\ell_\infty$ convergence rates of k nearest neighbor density estimation method. Our analysis includes two different cases depending on whether the support set is bounded or not. In the first case, the…

Nearest neighbor methods are a popular class of nonparametric estimators with several desirable properties, such as adaptivity to different distance scales in different regions of space. Prior work on convergence rates for nearest neighbor…

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…

This paper studies the minimax rate of nonparametric conditional density estimation under a weighted absolute value loss function in a multivariate setting. We first demonstrate that conditional density estimation is impossible if one only…

We consider the problem of minimax estimation of the entropy of a density over Lipschitz balls. Dropping the usual assumption that the density is bounded away from zero, we obtain the minimax rates $(n\ln n)^{-s/(s+d)} + n^{-1/2}$ for…

We investigate Bayesian nonparametric density estimation via orthogonal polynomial expansions in weighted Sobolev spaces. A core challenge is establishing minimax optimal posterior convergence rates, especially for densities on unbounded…

Let $X\in \mathbb{R}^p$ and $Y\in \mathbb{R}$ be two random variables. We estimate the conditional covariance matrix $\mathrm{Cov}\left(\mathrm{E}\left[\boldsymbol{X}\vert Y\right]\right)$ applying a plug-in kernel-based algorithm to its…

In this paper, we investigate the statistical convergence rate of a Bayesian low-rank tensor estimator. Our problem setting is the regression problem where a tensor structure underlying the data is estimated. This problem setting occurs in…

Consider the problem of estimating the $\gamma$-level set $G^*_{\gamma}=\{x:f(x)\geq\gamma\}$ of an unknown $d$-dimensional density function $f$ based on $n$ independent observations $X_1,...,X_n$ from the density. This problem has been…

We show that DBSCAN can estimate the connected components of the $\lambda$-density level set $\{ x : f(x) \ge \lambda\}$ given $n$ i.i.d. samples from an unknown density $f$. We characterize the regularity of the level set boundaries using…

The log-concave maximum likelihood estimator of a density on the real line based on a sample of size $n$ is known to attain the minimax optimal rate of convergence of $O(n^{-4/5})$ with respect to, e.g., squared Hellinger distance. In this…

We consider nonparametric maximum-likelihood estimation of a log-concave density in case of interval-censored, right-censored and binned data. We allow for the possibility of a subprobability density with an additional mass at $+\infty$,…

We tackle the problem of high-dimensional nonparametric density estimation by taking the class of log-concave densities on $\mathbb{R}^p$ and incorporating within it symmetry assumptions, which facilitate scalable estimation algorithms and…

We consider the problem of estimating smooth integrated functionals of a monotone nonincreasing density $f$ on $[0,\infty)$ using the nonparametric maximum likelihood based plug-in estimator. We find the exact asymptotic distribution of…

Based on the Hilb type formula between Jacobi polynomials and Bessel functions, optimal decay rates on Jacobi expansion coefficients are derived, by applying van der Corput type lemmas, for functions of logarithmatic singularities, which…

We consider the problem of non-parametric density estimation of a random environment from the observation of a single trajectory of a random walk in this environment. We first construct a density estimator using the beta-moments. We then…