Related papers: $\beta$-Divergence loss for the kernel density est…
We define a new bandwidth-dependent kernel density estimator that improves existing convergence rates for the bias, and preserves that of the variation, when the error is measured in $L_1$. No additional assumptions are imposed to the…
Length-biased data are a particular case of weighted data, which arise in many situations: biomedicine, quality control or epidemiology among others. In this paper we study the theoretical properties of kernel density estimation in the…
In the context of estimating local modes of a conditional density based on kernel density estimators, we show that existing bandwidth selection methods developed for kernel density estimation are unsuitable for mode estimation. We propose…
Kernel estimation techniques, such as mean shift, suffer from one major drawback: the kernel bandwidth selection. The bandwidth can be fixed for all the data set or can vary at each points. Automatic bandwidth selection becomes a real…
We consider bandwidth matrix selection for kernel density estimators (KDEs) of density level sets in $\mathbb{R}^d$, $d \ge 2$. We also consider estimation of highest density regions, which differs from estimating level sets in that one…
It is a common practice to evaluate probability density function or matter spatial density function from statistical samples. Kernel density estimation is a frequently used method, but to select an optimal bandwidth of kernel estimation,…
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…
It is shown that, for kernel-based classification with univariate distributions and two populations, optimal bandwidth choice has a dichotomous character. If the two densities cross at just one point, where their curvatures have the same…
The Beta kernel estimator offers a theoretically superior alternative to the Gaussian kernel for unit interval data, eliminating boundary bias without requiring reflection or transformation. However, its adoption remains limited by the lack…
In the this paper, the authors propose to estimate the density of a targeted population with a weighted kernel density estimator (wKDE) based on a weighted sample. Bandwidth selection for wKDE is discussed. Three mean integrated squared…
Given a sample $\{X_i\}_{i=1}^n$ from $f_X$, we construct kernel density estimators for $f_Y$, the convolution of $f_X$ with a known error density $f_{\epsilon}$. This problem is known as density estimation with Berkson error and has…
Kernel density estimation is a key component of a wide variety of algorithms in machine learning, Bayesian inference, stochastic dynamics and signal processing. However, the unsupervised density estimation technique requires tuning a…
We consider estimating the density of a response conditioning on an error-prone covariate. Motivated by two existing kernel density estimators in the absence of covariate measurement error, we propose a method to correct the existing…
New bandwidth selectors for kernel density estimation with directional data are presented in this work. These selectors are based on asymptotic and exact error expressions for the kernel density estimator combined with mixtures of von Mises…
We are interested in the nonparametric estimation of the probability density of price returns, using the kernel approach. The output of the method heavily relies on the selection of a bandwidth parameter. Many selection methods have been…
We investigate the discrepancy principle for choosing smoothing parameters for kernel density estimation. The method is based on the distance between the empirical and estimated distribution functions. We prove some new positive and…
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…
In the context of kernel density estimation, we give a characterization of the kernels for which the parametric mean integrated squared error rate $n^{-1}$ may be obtained, where $n$ is the sample size. Also, for the cases where this rate…
Averaging provides an alternative to bandwidth selection for density kernel estimation. We propose a procedure to combine linearly several kernel estimators of a density obtained from different, possibly data-driven, bandwidths. The method…
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.…