Pointwise deconvolution with unknown error distribution

Comte, Fabienne; Lacour, Claire

doi:10.1016/j.crma.2010.02.012

Cited by 5 publications

(3 citation statements)

References 10 publications

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“…where G denotes a regular grid on In application, we also need to evaluate the density estimatorf X,n (•) over a grid of points of X so that probability estimates can be obtained by numerically integratingf X,n (•). This is a different matter than the problem of computingf X,n (•) at a single point x, see Comte and Lacour (2010). For that purpose, we carry out density estimationf X,n (x) on a regular grid of points x, say on…”

Section: Choice Of Kernel Functionmentioning

confidence: 99%

Bivariate Kernel Deconvolution with Panel Data

et al. 2020

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We consider estimation of the density of a multivariate response, that is not observed directly but only through measurements contaminated by additive error. Our focus is on the realistic sampling case of bivariate panel data (repeated contaminated bivariate measurements on each sample unit) with an unknown error distribution. Several factors can affect the performance of kernel deconvolution density estimators, including the choice of the kernel and the estimation approach of the unknown error distribution. As the choice of the kernel function is critically important, the class of flat-top kernels can have advantages over more commonly implemented alternatives. We describe different approaches for density estimation with multivariate panel responses, and investigate their performance through simulation. We examine competing kernel functions and describe a flat-top kernel that has not been used in deconvolution problems. Moreover, we study several nonparametric options for estimating the unknown error distribution. Finally, we also provide guidelines to the numerical implementation of kernel deconvolution in higher sampling dimensions.

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Section: Choice Of Kernel Functionmentioning

confidence: 99%

Bivariate Kernel Deconvolution with Panel Data

et al. 2020

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“…Alternatively, one can consider a framework with panel data [Neu07]. Finally, one can assume the availability of an additional sample from the error density (e.g., [DH93,Joh09,CL10,CL11]) to guarantee identifiability and enable inference. In this paper, we will stick to this last option.…”

Section: Introductionmentioning

confidence: 99%

Nonparametric intensity estimation from noisy observations of a Poisson process under unknown error distribution

Kroll

2019

Metrika

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We consider the nonparametric estimation of the intensity function of a Poisson point process in a circular model from indirect observations N1, . . . , Nn. These observations emerge from hidden point process realizations with the target intensity through contamination with additive error. In case that the error distribution can only be estimated from an additional sample Y1, . . . , Ym we derive minimax rates of convergence with respect to the sample sizes n and m under abstract smoothness conditions and propose an orthonormal series estimator which attains the optimal rate of convergence. The performance of the estimator depends on the correct specification of a dimension parameter whose optimal choice relies on smoothness characteristics of both the intensity and the error density. We propose a data-driven choice of the dimension parameter based on model selection and show that the adaptive estimator attains the minimax optimal rate.

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“…In application, we also need to evaluate the density estimatorf X,n (·) over a grid of points of X so that probability estimates can be obtained by numerically integratingf X,n (·). This is a different matter than the problem of computingf X,n (·) at a single point x, see Comte and Lacour (2010). For that purpose, we carry out density estimationf X,n (x) on a regular grid of and Swarztrauber (1994).…”

Section: Numerical Implementationmentioning

confidence: 99%

Kernel deconvolution density estimation

Basulto-Elias

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Pointwise deconvolution with unknown error distribution

Cited by 5 publications

References 10 publications

Bivariate Kernel Deconvolution with Panel Data

Bivariate Kernel Deconvolution with Panel Data

Nonparametric intensity estimation from noisy observations of a Poisson process under unknown error distribution

Kernel deconvolution density estimation

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