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We are studying the problem of estimating density in a wide range of metric spaces, including the Euclidean space, the sphere, the ball, and various Riemannian manifolds. Our framework involves a metric space with a doubling measure and a…

Statistics Theory · Mathematics 2023-04-04 Galatia Cleanthous , Athanasios G. Georgiadis , Philip A. White

In recent years, kernel density estimation has been exploited by computer scientists to model machine learning problems. The kernel density estimation based approaches are of interest due to the low time complexity of either O(n) or…

Machine Learning · Statistics 2007-10-16 Yen-Jen Oyang , Darby Tien-Hao Chang , Yu-Yen Ou , Hao-Geng Hung , Chih-Peng Wu , Chien-Yu Chen

Density estimation in high-dimensional settings is an important and challenging statistical problem.Traditional methods based on kernel smoothing are inefficient in high dimensions due to the difficulties in specifying appropriate…

Machine Learning · Statistics 2026-05-14 Ruitong Zhang , Ke Deng

We estimate the derivative of a probability density function defined on $[0,\infty)$. For this purpose, we choose the class of kernel estimators with asymmetric gamma kernel functions. The use of gamma kernels is fruitful due to the fact…

Statistics Theory · Mathematics 2015-02-10 L. A. Markovich

This study proposes multivariate kernel density estimation by stagewise minimization algorithm based on $U$-divergence and a simple dictionary. The dictionary consists of an appropriate scalar bandwidth matrix and a part of the original…

Machine Learning · Statistics 2021-08-11 Kiheiji Nishida , Kanta Naito

Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and…

Kernel density estimation (KDE) is integral to a range of generative and discriminative tasks in machine learning. Drawing upon tools from the multidimensional calculus of variations, we derive an optimal weight function that reduces bias…

Machine Learning · Computer Science 2023-11-07 Sangwoong Yoon , Frank C. Park , Gunsu S Yun , Iljung Kim , Yung-Kyun Noh

We study the worst case error of kernel density estimates via subset approximation. A kernel density estimate of a distribution is the convolution of that distribution with a fixed kernel (e.g. Gaussian kernel). Given a subset (i.e. a point…

Computational Geometry · Computer Science 2012-04-05 Jeff M. Phillips

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…

Statistics Theory · Mathematics 2011-11-22 J. E. Chacón , J. Montanero , A. G. Nogales

The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for…

Human-Computer Interaction · Computer Science 2017-09-14 Yan Zheng , Yi Ou , Alexander Lex , Jeff M. Phillips

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…

A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance. These pencils arise when…

Statistics Theory · Mathematics 2015-10-02 Piero Barone

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…

Methodology · Statistics 2011-11-28 Bin Wang , Xiaofeng Wang

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…

Information Theory · Computer Science 2017-02-13 Weihao Gao , Sewoong Oh , Pramod Viswanath

Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…

Machine Learning · Computer Science 2021-06-29 Boris Muzellec , Francis Bach , Alessandro Rudi

Kernel density estimation (KDE) is one of the most widely used nonparametric density estimation methods. The fact that it is a memory-based method, i.e., it uses the entire training data set for prediction, makes it unsuitable for most…

Machine Learning · Computer Science 2022-08-08 Joseph A. Gallego , Juan F. Osorio , Fabio A. González

We consider the problem of estimating the density of observations taking values in classical or nonclassical spaces such as manifolds and more general metric spaces. Our setting is quite general but also sufficiently rich in allowing the…

Probability · Mathematics 2019-02-12 G. Cleanthous , A. Georgiadis , G. Kerkyacharian , P. Petrushev , D. Picard

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…

Statistics Theory · Mathematics 2008-12-18 Aurore Delaigle , Alexander Meister

Local polynomial density (LPD) estimators are widely used for inference on boundary features of the density function. Contrary to conventional wisdom, we show that kernel choice substantially affects efficiency. Theory, simulations, and…

Econometrics · Economics 2026-01-08 Shunsuke Imai , Yuta Okamoto

This paper proposes nonparametric kernel-smoothing estimation for panel data to examine the degree of heterogeneity across cross-sectional units. We first estimate the sample mean, autocovariances, and autocorrelations for each unit and…

Econometrics · Economics 2019-05-28 Ryo Okui , Takahide Yanagi