Limit Distribution of Convex-Hull Estimators of Boundaries - Seok-Oh Jeong; Byeong U. Park (Humboldt-Universität zu Berlin, Center for Applied Statistics and Economics (CASE), 2004)
Given n independent and identically distributed observations in a set G 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. It is particularly important in econometrics. The convex-hull estimator of a boundary or frontier is very popular in econometrics, where it is a cornerstone of a method known as `data envelope analysis or DEA. 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.
Keywords: 330; Convex-hull; free disposal hull; frontier function; data envelope analysis; productivity analysis; rate of convergence