ASYMPTOTIC DISTRIBUTION OF CONICAL-HULL ESTIMATORS OF DIRECTIONAL EDGES

By Byeong U. Park, Seok-Oh Jeong, Léopold Simar. 2010

74 citations recorded by the source corpus.

Non-parametric data envelopment analysis (DEA) estimators have been widely applied in analysis of productive efficiency. Typically they are deﬁned in terms of convex-hulls of the observed combinations of inputs × outputs in a sample of enterprises. The shape of the convex-hull relies on hypothesis on the shape of the technology, deﬁned as the boundary of the set of technically attainable points in the inputs × outputs space. So far, only the statistical properties of the smallest convex polyhedron enveloping the data points has been considered, which corresponds to a situation where the technology presents varying returns-to-scale (VRS). This paper analyzes the case where the most common constant returns-to-scale (CRS) hypothesis is assumed. Here the DEA is deﬁned as the smallest conical-hull with vertex at the origin enveloping the cloud of observed points. In this paper we determine the asymptotic properties of this estimator, showing that the rate of convergence is better than for the VRS estimator. We derive also its asymptotic sampling distribution, with a practical way to simulate it. This allows to deﬁne a bias-corrected estimator and to build conﬁdence intervals for the frontier. We compare in a simulated example the bias-corrected estimator with the original conical-hull estimator, and show its superiority in terms of median squared error.

Subfields: Economics and Econometrics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/064b9fd79a159315c10ecf1d9b47a7705964067e

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Citations in the corpus

Estimation and Inference in Nonparametric Frontier Models: Recent Developments and Perspectives (2013, methodology): “6) were known, or alternatively, one could allow ψ(Z,β) and the distribution of to be nonparametric and estimate ψ(·) using the local likelihood method discussed by Park et al. (2008). Unfortunately, however, the λi are not observed.”
Inference by the m out of n bootstrap in nonparametric frontier models (2011, background): “If in addition P = V(P), then θ CRS (x, y) is a consistent estimator of θ(x, y | P), with convergence rate n −2/(p+q) (Park et al., 2010).”
Testing Hypotheses in Nonparametric Models of Production (2016, background): “…results about properties of DEA and FDH estimators, including Korostelev, Simar, and Tsybakov (1995a, 1995b), Park, Simar, and Weiner (2000), Park, Jeong, and Simar (2010), Kneip, Park, and Simar (1998), Kneip, Simar, and Wilson (2008, 2011), Gijbels et al. (1999), and Wilson (2011), it is…”
Two-stage DEA: caveat emptor (2011, methodology): “The properties of DEA estimators have been developed by Korostelev et al. (1995a, 1995b), Kneip et al. (1998), Kneip et al. (2008, 2010), Park et al. (2010) and Simar and Wilson (2010b), and depend on assumptions about returns to scale.”