Estimation of boundary and discontinuity points in deconvolution problems

A Delaigle, I Gijbels

Research output: Contribution to journalArticle (Academic Journal)peer-review

26 Citations (Scopus)


We consider estimation of the boundary of the support of a density function when only a contaminated sample from the density is available. This estimation problem is a necessary step when estimating a density with unknown support, different from the whole real line, since then modifications of the usual kernel type estimators are needed for consistent estimation of the density at the endpoints of its support. Boundary estimation is also of interest on its own, since it is the basic problem in, for example, frontier estimation in efficiency analysis in econometrics. The method proposed in this paper can also be used for estimating locations of discontinuity points of a density in the same deconvolution context. We establish the limiting distribution of the proposed estimator as well as approximate expressions for its mean squared error and deduce rates of convergence of the estimator; The finite sample performance of the procedure is investigated via simulation.
Translated title of the contributionEstimation of boundary and discontinuity points in deconvolution problems
Original languageEnglish
Pages (from-to)773 - 788
Number of pages16
JournalStatistica Sinica
Volume16 (3)
Publication statusPublished - Jul 2006

Bibliographical note

Publisher: Statistica Sinica
Other identifier: IDS number 078SO

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