Related papers: Density deconvolution from repeated measurements w…

Let $X$ and $Y$ be two independent identically distributed random variables with density $p(x)$ and $Z=\alpha X+\beta Y$ for some constants $\alpha>0$ and $\beta>0$. We consider the problem of estimating $p(x)$ by means of the samples from…

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…

Consider the regression problem where the response $Y\in\mathbb{R}$ and the covariate $X\in\mathbb{R}^d$ for $d\geq 1$ are \textit{unmatched}. Under this scenario, we do not have access to pairs of observations from the distribution of $(X,…

We study the problem nonparametric classification with repeated observations. Let $\bX$ be the $d$ dimensional feature vector and let $Y$ denote the label taking values in $\{1,\dots ,M\}$. In contrast to usual setup with large sample size…

This paper considers convolution equations that arise from problems such as measurement error and non-parametric regression with errors in variables with independence conditions. The equations are examined in spaces of generalized functions…

Density deconvolution is the task of estimating a probability density function given only noise-corrupted samples. We can fit a Gaussian mixture model to the underlying density by maximum likelihood if the noise is normally distributed, but…

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…

In the context of regressing a response $Y$ on a predictor $X$, we consider estimating the local modes of the distribution of $Y$ given $X=x$ when $X$ is prone to measurement error. We propose two nonparametric estimation methods, with one…

Nonparametric estimation of a mixing density based on observations from the corresponding mixture is a challenging statistical problem. This paper surveys the literature on a fast, recursive estimator based on the predictive recursion…

Let $X_1,..., X_n$ be i.i.d.\ copies of a random variable $X=Y+Z,$ where $ X_i=Y_i+Z_i,$ and $Y_i$ and $Z_i$ are independent and have the same distribution as $Y$ and $Z,$ respectively. Assume that the random variables $Y_i$'s are…

Deconvolution is the important problem of estimating the distribution of a quantity of interest from a sample with additive measurement error. Nearly all methods in the literature are based on Fourier transformation because it is…

We consider the problem of multivariate density deconvolution where the distribution of a random vector needs to be estimated from replicates contaminated with conditionally heteroscedastic measurement errors. We propose a conceptually…

In the convolution model $Z\_i=X\_i+ \epsilon\_i$, we give a model selection procedure to estimate the density of the unobserved variables $(X\_i)\_{1 \leq i \leq n}$, when the sequence $(X\_i)\_{i \geq 1}$ is strictly stationary but not…

The paper discusses the estimation of a continuous density function of the target random field $X_{\bf{i}}$, $\bf{i}\in \mathbb {Z}^N$ which is contaminated by measurement errors. In particular, the observed random field $Y_{\bf{i}}$,…

Bayesian density deconvolution using nonparametric prior distributions is a useful alternative to the frequentist kernel based deconvolution estimators due to its potentially wide range of applicability, straightforward uncertainty…

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…

We consider testing statistical hypotheses about densities of signals in deconvolution models. A new approach to this problem is proposed. We constructed score tests for the deconvolution with the known noise density and efficient score…

In reliability theory and survival analysis, observed data are often weakly dependent and subject to additive measurement errors. Such contamination arises when the underlying data are neither independent nor strongly mixed but instead…

In this paper, we consider a partial deconvolution kernel estimator for nonparametric regression when some covariates are measured with error while others are observed without error. We focus on a general and realistic setting in which the…

This paper considers the problem of adaptive estimation of a mean pattern in a randomly shifted curve model. We show that this problem can be transformed into a linear inverse problem, where the density of the random shifts plays the role…