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Article: Deconvolution estimation of mixture distributions with boundaries

TitleDeconvolution estimation of mixture distributions with boundaries
Authors
KeywordsBoundary efiect
Penalization
Measurement error
Mixture distribution
Maximum likelihood
Sieve method
Issue Date2013
Citation
Electronic Journal of Statistics, 2013, v. 7, n. 1, p. 323-341 How to Cite?
AbstractIn this paper, motivated by an important problem in evolutionary biology, we develop two sieve type estimators for distributions that are mixtures of a finite number of discrete atoms and continuous distributions under the framework of measurement error models. While there is a large literature on deconvolution problems, only two articles have previously addressed the problem taken up in our article, and they use relatively standard Fourier deconvolution. As a result the estimators suggested in those two articles are degraded seriously by boundary efiects and negativity. A major contribution of our article is correct handling of boundary efiects; our method is asymptotically unbiased at the boundaries, and also is guaranteed to be nonnegative. We use roughness penalization to improve the smoothness of the resulting estimator and reduce the estimation variance. We illustrate the performance of the proposed estimators via our real driving application in evolutionary biology and two simulation studies. Furthermore, we establish asymptotic properties of the proposed estimators.
Persistent Identifierhttp://hdl.handle.net/10722/219692
ISSN
2015 Impact Factor: 0.736
2015 SCImago Journal Rankings: 1.661

 

DC FieldValueLanguage
dc.contributor.authorLee, Mihee-
dc.contributor.authorHall, Peter-
dc.contributor.authorShen, Haipeng-
dc.contributor.authorMarron, J. S.-
dc.contributor.authorTolle, Jon-
dc.contributor.authorBurch, Christina-
dc.date.accessioned2015-09-23T02:57:44Z-
dc.date.available2015-09-23T02:57:44Z-
dc.date.issued2013-
dc.identifier.citationElectronic Journal of Statistics, 2013, v. 7, n. 1, p. 323-341-
dc.identifier.issn1935-7524-
dc.identifier.urihttp://hdl.handle.net/10722/219692-
dc.description.abstractIn this paper, motivated by an important problem in evolutionary biology, we develop two sieve type estimators for distributions that are mixtures of a finite number of discrete atoms and continuous distributions under the framework of measurement error models. While there is a large literature on deconvolution problems, only two articles have previously addressed the problem taken up in our article, and they use relatively standard Fourier deconvolution. As a result the estimators suggested in those two articles are degraded seriously by boundary efiects and negativity. A major contribution of our article is correct handling of boundary efiects; our method is asymptotically unbiased at the boundaries, and also is guaranteed to be nonnegative. We use roughness penalization to improve the smoothness of the resulting estimator and reduce the estimation variance. We illustrate the performance of the proposed estimators via our real driving application in evolutionary biology and two simulation studies. Furthermore, we establish asymptotic properties of the proposed estimators.-
dc.languageeng-
dc.relation.ispartofElectronic Journal of Statistics-
dc.subjectBoundary efiect-
dc.subjectPenalization-
dc.subjectMeasurement error-
dc.subjectMixture distribution-
dc.subjectMaximum likelihood-
dc.subjectSieve method-
dc.titleDeconvolution estimation of mixture distributions with boundaries-
dc.typeArticle-
dc.description.natureLink_to_subscribed_fulltext-
dc.identifier.doi10.1214/13-EJS774-
dc.identifier.scopuseid_2-s2.0-84873870030-
dc.identifier.volume7-
dc.identifier.issue1-
dc.identifier.spage323-
dc.identifier.epage341-

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