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Statistica Sinica 16(2006), 773-788



A. Delaigle and I. Gijbels

University of California at San Diego and Katholieke Universiteit of Leuven

Abstract: 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.

Key words and phrases: Asymptotic distribution, boundary points, deconvolution problem, density estimation, diagnostic function, discontinuity points, endpoints, rates of convergence.

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