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Related papers: On estimation of analytic density in L_p

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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

We consider the problem of estimating the predictive density of future observations from a non-parametric regression model. The density estimators are evaluated under Kullback--Leibler divergence and our focus is on establishing the exact…

Statistics Theory · Mathematics 2010-10-12 Xinyi Xu , Feng Liang

This is the second part of the research project initiated in Cleanthous et al (2024). We deal with the problem of the adaptive estimation of the $\mathbb{L}_2$-norm of a probability density on $\mathbb{R}^d$, $d\geq 1$, from independent…

Statistics Theory · Mathematics 2024-05-28 Galatia Cleanthous , Athanasios G. Georgiadis , Oleg V. Lepski

This paper considers the problem of $L^p$-estimates for a certain multilinear functional involving integration against a kernel with the structure of a determinant. Examples of such objects are ubiquitous in the study of Fourier restriction…

Classical Analysis and ODEs · Mathematics 2009-11-09 Philip T. Gressman

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 $X$…

Statistics Theory · Mathematics 2015-05-15 Gilles Rebelles

This paper continues the research started in \cite{LW16}. In the framework of the convolution structure density model on $\bR^d$, we address the problem of adaptive minimax estimation with $\bL_p$--loss over the scale of anisotropic…

Statistics Theory · Mathematics 2017-04-17 Oleg Lepski , Thomas Willer

We estimate on a compact interval densities with isolated irregularities, such as discontinuities or discontinuities in some derivatives. From independent and identically distributed observations we construct a kernel estimator with…

Statistics Theory · Mathematics 2024-07-16 Céline Duval , Émeline Schmisser

We study the problem of estimating the joint probability mass function (pmf) over two random variables. In particular, the estimation is based on the observation of $m$ samples containing both variables and $n$ samples missing one fixed…

Statistics Theory · Mathematics 2024-05-16 Hasan Sabri Melihcan Erol , Lizhong Zheng

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…

Statistics Theory · Mathematics 2025-05-30 Jack Kendrick

This paper presents a novel approach for pointwise estimation of multivariate density functions on known domains of arbitrary dimensions using nonparametric local polynomial estimators. Our method is highly flexible, as it applies to both…

Statistics Theory · Mathematics 2025-07-22 Karine Bertin , Nicolas Klutchnikoff , Frédéric Ouimet

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…

Data Analysis, Statistics and Probability · Physics 2015-02-27 Anton Poluektov

Evaluating treatments received by one population for application to a different target population of scientific interest is a central problem in causal inference from observational studies. We study the minimax linear estimator of the…

Statistics Theory · Mathematics 2021-03-01 David A. Hirshberg , Arian Maleki , Jose R. Zubizarreta

The performance of kernel density estimators is usually studied via Taylor expansions and asymptotic approximation arguments, in which the bandwidth parameter tends to zero with increasing sample size. In contrast, this paper focusses…

Statistics Theory · Mathematics 2026-02-25 Nils Lid Hjort , Nikolai G. Ushakov

We consider the problem of estimating the probability density function of a circular random variable observed under censoring. To this end, we introduce a projection estimator constructed via a regression approach on linear sieves. We first…

Statistics Theory · Mathematics 2025-12-09 Nicolas Conanec , Claire Lacour , Thanh Mai Pham Ngoc

This paper introduces a probability density estimator based on Green's function identities. A density model is constructed under the sole assumption that the probability density is differentiable. The method is implemented as a binary…

Machine Learning · Statistics 2012-08-22 Peter Kovesarki , Ian C. Brock , A. Elizabeth Nuncio Quiroz

This article is dedicated to the estimation of the regression function when the explanatory variable is a weakly dependent process whose correlation coefficient exhibits exponential decay and has a known bounded density function. The…

Statistics Theory · Mathematics 2025-07-17 Karine Bertin , Lisandro Fermin , Miguel Padrino

This study intends to introduce kernel mean embedding of probability measures over infinite-dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of…

Statistics Theory · Mathematics 2020-11-05 Saeed Hayati , Kenji Fukumizu , Afshin Parvardeh

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

We study the adaptive minimax estimation of non-linear integral functionals of a density and extend the results obtained for linear and quadratic functionals to general functionals. The typical rate optimal non-adaptive minimax estimators…

Statistics Theory · Mathematics 2016-01-12 Rajarshi Mukherjee , Eric Tchetgen Tchetgen , James Robins

We derive an upper bound on the local Rademacher complexity of $\ell_p$-norm multiple kernel learning, which yields a tighter excess risk bound than global approaches. Previous local approaches aimed at analyzed the case $p=1$ only while…

Machine Learning · Statistics 2011-03-07 Marius Kloft , Gilles Blanchard