On Convex Boundary Estimation

  • Seok-Oh Jeong
  • Byeong U. Park


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.


Data Envelopment Analysis Boundary Function Asymptotic Distribution Production Frontier Boundary Estimation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of StatisticsHankuk University of Foreign StudiesYong-InSouth Korea
  2. 2.Department of StatisticsSeoul National UniversitySeoulSouth Korea

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