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1997-08-01Buch DOI: 10.18452/3709
On Estimation of Monotone and Concave Frontier Functions
dc.contributor.authorGijbels, I.
dc.contributor.authorMammen, Enno
dc.contributor.authorPark, Byeong U.
dc.contributor.authorSimar, Léopold
dc.date.accessioned2017-06-15T21:52:23Z
dc.date.available2017-06-15T21:52:23Z
dc.date.created2006-01-20
dc.date.issued1997-08-01
dc.identifier.issn1436-1086
dc.identifier.urihttp://edoc.hu-berlin.de/18452/4361
dc.description.abstractWhen 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.eng
dc.language.isoeng
dc.publisherHumboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät
dc.subjectconfidence intervaleng
dc.subjectAsymptotic distributioneng
dc.subjectbias correctioneng
dc.subjectdata envelopment analysiseng
dc.subjectdensity supporteng
dc.subjectfrontier functioneng
dc.subject.ddc330 Wirtschaft
dc.titleOn Estimation of Monotone and Concave Frontier Functions
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-10056435
dc.identifier.doihttp://dx.doi.org/10.18452/3709
dc.subject.dnb17 Wirtschaft
local.edoc.container-titleSonderforschungsbereich 373: Quantification and Simulation of Economic Processes
local.edoc.pages25
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-volume1998
local.edoc.container-issue9
local.edoc.container-year1998
local.edoc.container-erstkatid2135319-0

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