Related papers: On deconvolution with repeated measurements
We consider deconvolution from repeated observations with unknown error distribution. So far, this model has mostly been studied under the additional assumption that the errors are symmetric. We construct an estimator for the non-symmetric…
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…
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…
We construct a density estimator and an estimator of the distribution function in the uniform deconvolution model. The estimators are based on inversion formulas and kernel estimators of the density of the observations and its derivative.…
We consider the problem of multivariate density deconvolution when the interest lies in estimating the distribution of a vector-valued random variable but precise measurements of the variable of interest are not available, observations…
Deconvolution is a statistical inverse problem to estimate the distribution of a random variable based on its noisy observations. Despite the extensive studies on the topic, deconvolution with unknown noise distribution remains as a…
Regression evaluation has been performed for decades. Some metrics have been identified to be robust against shifting and scaling of the data but considering the different distributions of data is much more difficult to address (imbalance…
In this paper we study the problem of density deconvolution under general assumptions on the measurement error distribution. Typically deconvolution estimators are constructed using Fourier transform techniques, and it is assumed that the…
In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…
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…
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,…
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…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
We consider a multiplicative deconvolution problem, in which the density $f$ or the survival function $S^X$ of a strictly positive random variable $X$ is estimated nonparametrically based on an i.i.d. sample from a noisy observation $Y =…
The present paper studies density deconvolution in the presence of small Berkson errors, in particular, when the variances of the errors tend to zero as the sample size grows. It is known that when the Berkson errors are present, in some…
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…
We construct a density estimator in the bivariate uniform deconvolution model. For this model we derive four inversion formulas to express the bivariate density that we want to estimate in terms of the bivariate density of the observations.…
It is a typical standard assumption in the density deconvolution problem that the characteristic function of the measurement error distribution is non-zero on the real line. While this condition is assumed in the majority of existing works…
Deconvolution is a fundamental inverse problem in signal processing and the prototypical model for recovering a signal from its noisy measurement. Nevertheless, the majority of model-based inversion techniques require knowledge on the…
In inverse problems, one attempts to infer spatially variable functions from indirect measurements of a system. To practitioners of inverse problems, the concept of "information" is familiar when discussing key questions such as which parts…