Related papers: Adaptation to inhomogeneous smoothness for densiti…
Variable kernel density estimation allows the approximation of a probability density by the mean of differently stretched and rotated kernels centered at given sampling points $y_n\in\mathbb{R}^d,\ n=1,\dots,N$. Up to now, the choice of the…
In this paper, we deal with nonparametric regression for circular data, meaning that observations are represented by points lying on the unit circle. We propose a kernel estimation procedure with data-driven selection of the bandwidth…
In the analysis of spatial point patterns on linear networks, a critical statistical objective is estimating the first-order intensity function, representing the expected number of points within specific subsets of the network. Typically,…
We introduce a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations blurred by independent noises. We consider the intermediate regime, where observations occur at…
We develop honest and locally adaptive confidence bands for probability densities. They provide substantially improved confidence statements in case of inhomogeneous smoothness, and are easily implemented and visualized. The article…
We are interested in the rate of consistency of kernel density estimators with respect to the weighted sup-norm determined by some unbounded weight function. This problem has been considered by Gine, Koltchinskii and Zinn (2004) for a…
Kernel Density Estimation is a very popular technique of approximating a density function from samples. The accuracy is generally well-understood and depends, roughly speaking, on the kernel decay and local smoothness of the true density.…
We discuss and compare various approaches to the problem of bandwidth selection for kernel estimators of intensity functions of spatial point processes. We also propose a new method based on the Campbell formula applied to the reciprocal…
It is shown that the Hall, Hu and Marron [Hall, P., Hu, T., and Marron J.S. (1995), Improved Variable Window Kernel Estimates of Probability Densities, {\it Annals of Statistics}, 23, 1--10] modification of Abramson's [Abramson, I. (1982),…
This paper is concerned with adaptive kernel estimation of the L\'evy density N(x) for bounded-variation pure-jump L\'evy processes. The sample path is observed at n discrete instants in the "high frequency" context (\Delta = \Delta(n)…
We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…
A kernel density estimator for data on the polysphere $\mathbb{S}^{d_1}\times\cdots\times\mathbb{S}^{d_r}$, with $r,d_1,\ldots,d_r\geq 1$, is presented in this paper. We derive the main asymptotic properties of the estimator, including mean…
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…
A new multivariate density estimator for stationary sequences is obtained by Fourier inversion of the thresholded empirical characteristic function. This estimator does not depend on the choice of parameters related to the smoothness of the…
Density regression provides a flexible strategy for modeling the distribution of a response variable $Y$ given predictors $\mathbf{X}=(X_1,\ldots,X_p)$ by letting that the conditional density of $Y$ given $\mathbf{X}$ as a completely…
In this paper, we address the problem of estimating a multidimensional density $f$ by using indirect observations from the statistical model $Y=X+\varepsilon$. Here, $\varepsilon$ is a measurement error independent of the random vector $X$…
This paper develops a novel approach to density estimation on a network. We formulate nonparametric density estimation on a network as a nonparametric regression problem by binning. Nonparametric regression using local polynomial…
The traditional kernel density estimator of an unknown density is by construction completely nonparametric, in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of…
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…
Density estimation and inference methods are widely used in empirical work. When the underlying distribution has compact support, conventional kernel-based density estimators are no longer consistent near or at the boundary because of their…