Density estimation in the uniform deconvolution model

P. Groeneboom; G. Jongbloed

doi:10.1111/1467-9574.00225

Density estimation in the uniform deconvolution model

P. Groeneboom
, G. Jongbloed

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

We consider the problem of estimating a probability density function based on data that are corrupted by noise from a uniform distribution. The (nonparametric) maximum likelihood estimator for the corresponding distribution function is well defined. For the density function this is not the case. We study two nonparametric estimators for this density. The first is a type of kernel density estimate based on the empirical distribution function of the observable data. The second is a kernel density estimate based on the MLE of the distribution function of the unobservable (uncorrupted) data. © VVS, 2003.

Original language	English
Pages (from-to)	136-157
Journal	Statistica Neerlandica : Journal of the Netherlands Society for Statistics and Operations Research
Volume	57
Issue number	1
DOIs	https://doi.org/10.1111/1467-9574.00225
Publication status	Published - 2003

Bibliographical note

MR2035863 Incomplete data: multiple imputation and model-based analysis (Utrecht, 2001)

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10.1111/1467-9574.00225

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title = "Density estimation in the uniform deconvolution model",

abstract = "We consider the problem of estimating a probability density function based on data that are corrupted by noise from a uniform distribution. The (nonparametric) maximum likelihood estimator for the corresponding distribution function is well defined. For the density function this is not the case. We study two nonparametric estimators for this density. The first is a type of kernel density estimate based on the empirical distribution function of the observable data. The second is a kernel density estimate based on the MLE of the distribution function of the unobservable (uncorrupted) data. {\textcopyright} VVS, 2003.",

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AB - We consider the problem of estimating a probability density function based on data that are corrupted by noise from a uniform distribution. The (nonparametric) maximum likelihood estimator for the corresponding distribution function is well defined. For the density function this is not the case. We study two nonparametric estimators for this density. The first is a type of kernel density estimate based on the empirical distribution function of the observable data. The second is a kernel density estimate based on the MLE of the distribution function of the unobservable (uncorrupted) data. © VVS, 2003.

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JF - Statistica Neerlandica : Journal of the Netherlands Society for Statistics and Operations Research

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ER -

Density estimation in the uniform deconvolution model

Abstract

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