Related papers: On multivariate associated kernels for smoothing g…
Multivariate nonnegative orthant data are real vectors bounded to the left by the null vector, and they can be continuous, discrete or mixed. We first review the recent relative variability indexes for multivariate nonnegative continuous…
Estimating expected polynomials of density functions from samples is a basic problem with numerous applications in statistics and information theory. Although kernel density estimators are widely used in practice for such functional…
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 show that the cumulative distribution function corresponding to a kernel density estimator with optimal bandwidth lies outside any confidence interval, around the empirical distribution function, with probability tending to 1 as the…
Computing a consensus object from a set of given objects is a core problem in machine learning and pattern recognition. One popular approach is to formulate it as an optimization problem using the generalized median. Previous methods like…
Allthough nonparametric kernel density estimation with bias reduce is nowadays a standard technique in explorative data-analysis, there is still a big dispute on how to assess the quality of the estimate and which choice of bandwidth is…
Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…
Important information concerning a multivariate data set, such as clusters and modal regions, is contained in the derivatives of the probability density function. Despite this importance, nonparametric estimation of higher order derivatives…
It is possible to approach regression analysis with random covariates from a semiparametric perspective where information is combined from multiple multivariate sources. The approach assumes a semiparametric density ratio model where…
This paper studies Kernel Density Estimation for a high-dimensional distribution $\rho(x)$. Traditional approaches have focused on the limit of large number of data points $n$ and fixed dimension $d$. We analyze instead the regime where…
In this paper, we present a comprehensive analysis of the posterior covariance field in Gaussian processes, with applications to the posterior covariance matrix. The analysis is based on the Gaussian prior covariance but the approach also…
We introduce a general method to prove uniform in bandwidth consistency of kernel-type function estimators. Examples include the kernel density estimator, the Nadaraya-Watson regression estimator and the conditional empirical process. Our…
Markov chain Monte Carlo samplers produce dependent streams of variates drawn from the limiting distribution of the Markov chain. With this as motivation, we introduce novel univariate kernel density estimators which are appropriate for the…
Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data…
In biomedical studies, we are often interested in the association between different types of covariates and the times to disease events. Because the relationship between the covariates and event times is often complex, standard survival…
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,…
We present a new smooth, Gaussian-like kernel that allows the kernel density estimate for an angular distribution to be exactly represented by a finite number of its Fourier series coefficients. Distributions of angular quantities, such as…
Accurate density estimation methodologies play an integral role in a variety of scientific disciplines, with applications including simulation models, decision support tools, and exploratory data analysis. In the past, histograms and kernel…
We construct a density estimator and an estimator of the distribution function in the uniform deconvolution model. The estimators are based on inversion formulas and kernel estimators of the density of the observations and its derivative.…
We study the kernel estimator of the transition density of bifurcating Markov chains. Under some ergodic and regularity properties, we prove that this estimator is consistent and asymptotically normal. Next, in the numerical studies, we…