On Convex Boundary Estimation

Seok-Oh Jeong () and Byeong U. Park ()
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Seok-Oh Jeong: Hankuk University of Foreign Studies, Department of Statistics
Byeong U. Park: Seoul National University, Department of Statistics

Chapter Chapter 9 in Exploring Research Frontiers in Contemporary Statistics and Econometrics, 2011, pp 189-200 from Springer

Abstract: 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.

Keywords: Data Envelopment Analysis; Boundary Function; Asymptotic Distribution; Production Frontier; Boundary Estimation (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7908-2349-3_9

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DOI: 10.1007/978-3-7908-2349-3_9

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