Related papers: Data-Based Optimal Bandwidth for Kernel Density Es…
We determine the expected error by smoothing the data locally. Then we optimize the shape of the kernel smoother to minimize the error. Because the optimal estimator depends on the unknown function, our scheme automatically adjusts to the…
For the purpose of maximum likelihood estimation of static parameters, we apply a kernel smoother to the particles in the standard SIR filter for non-linear state space models with additive Gaussian observation noise. This reduces the Monte…
Graph spectral techniques for measuring graph similarity, or for learning the cluster number, require kernel smoothing. The choice of kernel function and bandwidth are typically chosen in an ad-hoc manner and heavily affect the resulting…
This tutorial provides a gentle introduction to kernel density estimation (KDE) and recent advances regarding confidence bands and geometric/topological features. We begin with a discussion of basic properties of KDE: the convergence rate…
This paper deals with the kernel density estimator based on the so-called sinc (or Fourier integral) kernel $K(x)=(\pi x)^{-1}\sin x$. We study in detail both asymptotic and finite sample properties of this estimator. It is shown that,…
We present a study of a kernel-based two-sample test statistic related to the Maximum Mean Discrepancy (MMD) in the manifold data setting, assuming that high-dimensional observations are close to a low-dimensional manifold. We characterize…
We study kernel-based estimation of nonparametric time-varying parameters (TVPs) in linear models. Our contributions are threefold. First, we establish consistency and asymptotic normality of the kernel-based estimator for a broad class of…
In this paper, we consider the nonparametric estimation of the multivariate probability density function and its partial derivative with a support on $[0,\infty)$. To this end we use the class of kernel estimators with asymmetric gamma…
We discuss properties of two methods for ascribing probabilities to the shape of a probability distribution. One is based on the idea of counting the number of modes of a bootstrap version of a standard kernel density estimator. We argue…
This paper develops a nonparametric density estimator with parametric overtones. Suppose $f(x,\theta)$ is some family of densities, indexed by a vector of parameters $\theta$. We define a local kernel smoothed likelihood function which for…
Empirical data can often be considered as samples from a set of probability distributions. Kernel methods have emerged as a natural approach for learning to classify these distributions. Although numerous kernels between distributions have…
Density estimation is a crucial component of many machine learning methods, and manifold learning in particular, where geometry is to be constructed from data alone. A significant practical limitation of the current density estimation…
Consider the nonparametric regression model Y=m(X)+E, where the function m is smooth but unknown, and E is independent of X. An estimator of the density of the error term E is proposed and its weak consistency is obtained. The contribution…
We present a new approach, kernel regression, to determine photometric redshifts for 399,929 galaxies in the Fifth Data Release of the Sloan Digital Sky Survey (SDSS). In our case, kernel regression is a weighted average of spectral…
Density level sets can be estimated using plug-in methods, excess mass algorithms or a hybrid of the two previous methodologies. The plug-in algorithms are based on replacing the unknown density by some nonparametric estimator, usually the…
We address the problem of density estimation with $\mathbb{L}_s$-loss by selection of kernel estimators. We develop a selection procedure and derive corresponding $\mathbb{L}_s$-risk oracle inequalities. It is shown that the proposed…
We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing…
A kernel based procedure for correcting experimental data for distortions due to the finite resolution and limited detector acceptance is presented. The unfolding problem is known to be an ill-posed problem that can not be solved without…
Modern empirical work in Regression Discontinuity (RD) designs often employs local polynomial estimation and inference with a mean square error (MSE) optimal bandwidth choice. This bandwidth yields an MSE-optimal RD treatment effect…
It is common, in deconvolution problems, to assume that the measurement errors are identically distributed. In many real-life applications, however, this condition is not satisfied and the deconvolution estimators developed for…