Large Sample Approximation of the Distribution for Convex‐Hull Estimators of Boundaries

S.‐O. Jeong and B. U. Park

Scandinavian Journal of Statistics, 2006, vol. 33, issue 1, 139-151

Abstract: Abstract. Given n independent and identically distributed observations in a set G = {(x, y) ∈ [0, 1]p × ℝ : 0 ≤ y ≤ g(x)} with an unknown function g, called a boundary or frontier, it is desired to estimate g from the observations. The problem has several important applications including classification and cluster analysis, and is closely related to edge estimation in image reconstruction. The convex‐hull estimator of a boundary or frontier is also very popular in econometrics, where it is a cornerstone of a method known as ‘data envelope analysis’. In this paper, we give a large sample approximation of the distribution of the convex‐hull estimator in the general case where p ≥ 1. We discuss ways of using the large sample approximation to correct the bias of the convex‐hull and the DEA estimators and to construct confidence intervals for the true function.

Date: 2006
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Citations: View citations in EconPapers (11)

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