Non-convex Technologies and Cost Functions: Definitions,Duality and Nonparametric Tests of Convexity |
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Authors: | Walter?Briec Email author" target="_blank">Kristiaan?KerstensEmail author Philippe Venden?Eeckaut |
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Institution: | (1) JEREM, Université de, Perpignan 54 Avenue Villeneuve, F-66000 Perpignan, France;(2) CNRS-LABORES, IESEG, 3 rue de la Digue, F-59800 Lille, France;(3) GREMARS, University of Lille, 3, Domaine Universitaire du “Pont de Bois”, BP, 149 F-59653 Villeneuve d’Ascq Cédex, France |
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Abstract: | This contribution is the first systematic attempt to develop a series of nonparametric, deterministic technologies and cost
functions without maintaining convexity. Specifically, we introduce returns to scale assumptions into an existing non-convex
technology and, dual to these technologies, define non-convex cost functions that are never lower than their convex counterparts.
Both non-convex technologies and cost functions (total, ray-average and marginal) are characterized by closed form expressions.
Furthermore, a local duality result is established between a local cost function and the input distance function. Finally,
nonparametric goodness-of-fit tests for convexity are developed as a first step towards making it a statistically testable
hypothesis.
An erratum to this article is available at . |
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Keywords: | nonparametric technologies and cost functions non-convexity nonparametric test of convexity |
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