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Recent advances have demonstrated the possibility of solving the deconvolution problem without prior knowledge of the noise distribution. In this paper, we study the repeated measurements model, where information is derived from multiple…

Statistics Theory · Mathematics 2024-09-04 Jérémie Capitao-Miniconi , Elisabeth Gassiat , Luc Lehéricy

We examine theoretical properties of the denoising score matching estimate. We model the density of observations with a nonparametric Gaussian mixture. We significantly relax the standard manifold assumption allowing the samples step away…

Machine Learning · Computer Science 2026-01-01 Konstantin Yakovlev , Nikita Puchkin

This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…

Machine Learning · Statistics 2026-05-06 Arnaud Vadeboncoeur , Mark Girolami , Andrew M. Stuart

Quantile estimation in deconvolution problems is studied comprehensively. In particular, the more realistic setup of unknown error distributions is covered. Our plug-in method is based on a deconvolution density estimator and is minimax…

Statistics Theory · Mathematics 2016-01-18 Itai Dattner , Markus Reiß , Mathias Trabs

The density ratio is an important metric for evaluating the relative likelihood of two probability distributions, with extensive applications in statistics and machine learning. However, existing estimation theories for density ratios often…

Machine Learning · Statistics 2025-04-03 Shuntuo Xu , Zhou Yu , Jian Huang

Over the last few years, debiased estimators have been proposed in order to establish rigorous confidence intervals for high-dimensional problems in machine learning and data science. The core argument is that the error of these estimators…

Signal Processing · Electrical Eng. & Systems 2024-07-19 Frederik Hoppe , Claudio Mayrink Verdun , Felix Krahmer , Marion I. Menzel , Holger Rauhut

We generalize the well-known mixtures of Gaussians approach to density estimation and the accompanying Expectation--Maximization technique for finding the maximum likelihood parameters of the mixture to the case where each data point…

Methodology · Statistics 2011-08-01 Jo Bovy , David W. Hogg , Sam T. Roweis

Via a simulation study we compare the finite sample performance of the deconvolution kernel density estimator in the supersmooth deconvolution problem to its asymptotic behaviour predicted by two asymptotic normality theorems. Our results…

Methodology · Statistics 2008-01-18 Bert van Es , Shota Gugushvili

The density deconvolution problem involves recovering a target density g from a sample that has been corrupted by noise. From the perspective of Le Cam's local asymptotic normality theory, we show that non-parametric density deconvolution…

Statistics Theory · Mathematics 2015-07-06 Stefan Wager

We propose an estimator of a concave cumulative distribution function under the measurement error model, where the non-negative variables of interest are perturbed by additive independent random noise. The estimator is defined as the least…

Statistics Theory · Mathematics 2026-03-03 Mohammed Es-Salih Benjrada , Cecile Durot , Tommaso Lando

Unlinked regression, in which covariates and responses are observed separately without known correspondence, has recently gained increasing attention. Deconvolution, on the other hand, is a fundamental and challenging problem in…

Statistics Theory · Mathematics 2026-05-19 Fadoua Balabdaoui , Antonio Di Noia , Cécile Durot

In many real applications, the distribution of measurement error could vary with each subject or even with each observation so the errors are heteroscedastic. In this paper, we propose a fast algorithm using a simulation-extrapolation…

Statistics Theory · Mathematics 2009-02-13 Xiao-Feng Wang , Jiayang Sun , Zhaozhi Fan

Uncertainty estimation is a key component in any deployed machine learning system. One way to evaluate uncertainty estimation is using "out-of-distribution" (OoD) detection, that is, distinguishing between the training data distribution and…

Machine Learning · Computer Science 2021-12-03 Haiwen Huang , Joost van Amersfoort , Yarin Gal

We consider a nonparametric regression model $Y=r(X)+\varepsilon$ with a random covariate $X$ that is independent of the error $\varepsilon$. Then the density of the response $Y$ is a convolution of the densities of $\varepsilon$ and…

Statistics Theory · Mathematics 2013-12-18 Anton Schick , Wolfgang Wefelmeyer

Many practical problems are related to the pointwise estimation of dis- tribution functions when data contains measurement errors. Motivation for these problems comes from diverse fields such as astronomy, reliability, quality control,…

Methodology · Statistics 2012-02-21 I. Dattner , B. Reiser

This work performs a non-asymptotic analysis of the generalized Lasso under the assumption of sub-exponential data. Our main results continue recent research on the benchmark case of (sub-)Gaussian sample distributions and thereby explore…

Statistics Theory · Mathematics 2023-01-18 Martin Genzel , Christian Kipp

Let $X_1,...,X_n$ be i.i.d. observations, where $X_i=Y_i+\sigma Z_i$ and $Y_i$ and $Z_i$ are independent. Assume that unobservable $Y$'s are distributed as a random variable $UV,$ where $U$ and $V$ are independent, $U$ has a Bernoulli…

Statistics Theory · Mathematics 2008-04-30 Bert van Es , Shota Gugushvili , Peter Spreij

Suppose $X_1,\dots, X_n$ is a random sample from a bounded and decreasing density $f_0$ on $[0,\infty)$. We are interested in estimating such $f_0$, with special interest in $f_0(0)$. This problem is encountered in various statistical…

Statistics Theory · Mathematics 2020-09-14 Geurt Jongbloed , Frank van der Meulen , Lixue Pang

This Note presents original rates of convergence for the deconvolution problem. We assume that both the estimated density and noise density are supersmooth and we compute the risk for two kinds of estimators.

Statistics Theory · Mathematics 2009-09-29 Claire Lacour

We consider drawing statistical inferences based on data subject to non-Gaussian measurement error. Unlike most existing methods developed under the assumption of Gaussian measurement error, the proposed strategy exploits hypercomplex…

Methodology · Statistics 2025-05-06 Nicholas W. Woolsey , Xianzheng Huang