English
Related papers

Related papers: Density deconvolution from repeated measurements w…

200 papers

In this paper we study the problem of pointwise density estimation from observations with multiplicative measurement errors. We elucidate the main feature of this problem: the influence of the estimation point on the estimation accuracy. In…

Methodology · Statistics 2018-07-13 Denis Belomestny , Alexander Goldenshluger

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

Several measures of non-convexity (departures from convexity) have been introduced in the literature, both for sets and functions. Some of them are of geometric nature, while others are more of topological nature. We address the statistical…

Statistics Theory · Mathematics 2022-11-23 Alejandro Cholaquidis , Ricardo Fraiman , Leonardo Moreno , Beatriz Pateiro-López

We consider the deconvolution problem for densities supported on a $(d-1)$-dimensional sphere with unknown center and unknown radius, in the situation where the distribution of the noise is unknown and without any other observations. We…

Statistics Theory · Mathematics 2022-03-08 Jérémie Capitao-Miniconi , Elisabeth Gassiat

We propose a linear algebraic framework for performing density estimation. It consists of three simple steps: convolving the empirical distribution with certain smoothing kernels to remove the exponentially large variance; compressing the…

Numerical Analysis · Mathematics 2025-10-29 Yifan Peng , Siyao Yang , Yuehaw Khoo , Daren Wang

A new maximum likelihood method for deconvoluting a continuous density with a positive lower bound on a known compact support in additive measurement error models with known error distribution using the approximate Bernstein type polynomial…

Methodology · Statistics 2018-01-30 Zhong Guan

The concept of biased data is well known and its practical applications range from social sciences and biology to economics and quality control. These observations arise when a sampling procedure chooses an observation with probability that…

Statistics Theory · Mathematics 2007-06-13 Sam Efromovich

When using the bootstrap in the presence of measurement error, we must first estimate the target distribution function; we cannot directly resample, since we do not have a sample from the target. These and other considerations motivate the…

Statistics Theory · Mathematics 2008-10-28 Peter Hall , Soumendra N. Lahiri

We consider noisy observations of a distribution with unknown support. In the deconvolution model, it has been proved recently [19] that, under very mild assumptions, it is possible to solve the deconvolution problem without knowing the…

Statistics Theory · Mathematics 2024-06-21 Jérémie Capitao-Miniconi , Elisabeth Gassiat , Luc Lehéricy

Many existing approaches for estimating parameters in settings with distributional shifts operate under an invariance assumption. For example, under covariate shift, it is assumed that $p(y|x)$ remains invariant. We refer to such…

Methodology · Statistics 2025-02-07 Yujin Jeong , Dominik Rothenhäusler

We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We…

Statistics Theory · Mathematics 2015-03-19 Johannes Schmidt-Hieber , Axel Munk , Lutz Duembgen

Frequentist-style large-sample properties of Bayesian posterior distributions, such as consistency and convergence rates, are important considerations in nonparametric problems. In this paper we give an analysis of Bayesian asymptotics…

Statistics Theory · Mathematics 2012-10-02 Ryan Martin , Liang Hong

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…

Statistics Theory · Mathematics 2011-12-25 Rawane Samb

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 the problem of estimating the density $g$ of identically distributed variables $X\_i$, from a sample $Z\_1, ..., Z\_n$ where $Z\_i=X\_i+\sigma\epsilon\_i$, $i=1, ..., n$ and $\sigma \epsilon\_i$ is a noise independent of $X\_i$…

Statistics Theory · Mathematics 2008-02-11 Fabienne Comte , Yves Rozenholc , Marie-Luce Taupin

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

We study the reknown deconvolution problem of recovering a distribution function from independent replicates (signal) additively contaminated with random errors (noise), whose distribution is known. We investigate whether a Bayesian…

Statistics Theory · Mathematics 2021-11-15 Judith Rousseau , Catia Scricciolo

We study full Bayesian procedures for sparse linear regression when errors have a symmetric but otherwise unknown distribution. The unknown error distribution is endowed with a symmetrized Dirichlet process mixture of Gaussians. For the…

Statistics Theory · Mathematics 2019-03-26 Minwoo Chae , Lizhen Lin , David B. Dunson

A new nonparametric estimator of a convex regression function in any dimension is proposed and its convergence properties are studied. We start by using any estimator of the regression function and we \emph{convexify} it by taking the…

Statistics Theory · Mathematics 2010-06-16 Néstor E. Aguilera , Liliana Forzani , Pedro Morin

This paper examines a stochastic deconvolution problem on compact symmetric spaces which is referred to as decompounding. This involves estimating the step distributions of a random walk, where in addition the number of steps between…

Statistics Theory · Mathematics 2026-04-20 Erik Kennerland