eprintid: 20865
rev_number: 12
eprint_status: archive
userid: 2326
dir: disk0/00/02/08/65
datestamp: 2016-06-07 07:31:16
lastmod: 2016-06-30 07:26:42
status_changed: 2016-06-07 07:31:16
type: workingPaper
metadata_visibility: show
creators_name: Gijbels, I.
creators_name: Park, Byeong U.
creators_name: Mammen, Enno
creators_name: Simar, Leopold
title: On Estimation of Monotone and Concave Frontier Functions
subjects: ddc-510
divisions: i-110400
keywords: Confidence interval, Asymptotic distribution, bias correction, data envelopment analysis
density support, frontier function
cterms_swd: Asymptotische Verteilung
note: Erschienen auch in: Discussion Papers, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1998,9
abstract: When analyzing the productivity of firms, one may want to compare how the firms transform a set of inputs x (typically labor, energy or capital) into an output y (typically a quantity of goods produced). The economic efficiency of a firm is then defined in terms of its ability of operating close to or on the production frontier which is the boundary of the production set. The frontier function gives the maximal level of output attainable by a firm for a given combination of its inputs. The efficiency of a firm may then be estimated via the distance between the attained production level and the optimal level given by the frontier function. From a statistical point of view, the frontier function may be viewed as the upper boundary of the support of the population of firms density in the input and output space. It is often reasonable to assume that the production frontier is a concave monotone function. Then, a famous estimator, in the univariate input and output case, is the data envelopment analysis (DEA) estimator which is the lowest concave monotone increasing function covering all sample points. This estimator is biased downwards since it never exceeds the true production frontier. In this paper we derive the asymptotic distribution of the DEA estimator, which enables us to assess the asymptotic bias and hence to propose an improved bias corrected estimator. This bias corrected estimator involves consistent estimation of the density function as well as of the second derivative of the production frontier. We also discuss briefly the construction of asymptotic confidence intervals. The finite sample performance of the bias corrected estimator is investigated via a simulation study and the procedure is illustrated for a real data example.
date: 1997-08-01
id_scheme: DOI
id_number: 10.11588/heidok.00020865
official_url: urn:nbn:de:kobv:11-10056435
schriftenreihe_cluster_id: sr-10a
schriftenreihe_order: 41
ppn_swb: 1657502899
own_urn: urn:nbn:de:bsz:16-heidok-208652
language: eng
bibsort: GIJBELSIONESTIMATI19970801
full_text_status: public
place_of_pub: Heidelberg
pages: 25
citation:   Gijbels, I. ; Park, Byeong U. ; Mammen, Enno ; Simar, Leopold  (1997) On Estimation of Monotone and Concave Frontier Functions.  [Working paper]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/20865/1/beitrag.41.pdf