# On Convex Boundary Estimation

Chapter

## 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
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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