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Erschienen in:
2012 | OriginalPaper | Buchkapitel
9. On Convex Boundary Estimation
verfasst von : Seok-Oh Jeong, Byeong U. Park
Erschienen in: Exploring Research Frontiers in Contemporary Statistics and Econometrics
Verlag: Physica-Verlag HD
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Abstract
Consider a convex set S of the form \(S =\{ (\mathbf{x},y) \in {\mathbb{R}}_{+}^{p} \times \{ {\mathbb{R}}_{+}\,\vert \,0 \leq y \leq g(\mathbf{x})\}\), where the function g stands for the upper boundary of the set S. Suppose that one is interested in estimating the set S (or equivalently, the boundary function g) based on a set of observations laid on S. Then one may think of building the convex-hull of the observations to estimate the set S, and the corresponding estimator of the boundary function g is given by the roof of the constructed convex-hull. In this chapter we give an overview of statistical properties of the convex-hull estimator of the boundary function g. Also, we discuss bias-correction and interval estimation with the convex-hull estimator.