Nonparametric quantile frontier estimation under shape restriction

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

21 Scopus Citations
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Original languageEnglish
Pages (from-to)671-678
Journal / PublicationEuropean Journal of Operational Research
Issue number3
Online published6 Jul 2013
Publication statusPublished - 1 Feb 2014


This paper proposes a shape-restricted nonparametric quantile regression to estimate the τ-frontier, which acts as a benchmark for whether a decision making unit achieves top τ efficiency. This method adopts a two-step strategy: first, identifying fitted values that minimize an asymmetric absolute loss under the nondecreasing and concave shape restriction; second, constructing a nondecreasing and concave estimator that links these fitted values. This method makes no assumption on the error distribution and the functional form. Experimental results on some artificial data sets clearly demonstrate its superiority over the classical linear quantile regression. We also discuss how to enforce constraints to avoid quantile crossings between multiple estimated frontiers with different values of τ. Finally this paper shows that this method can be applied to estimate the production function when one has some prior knowledge about the error term. © 2013 Elsevier B.V. All rights reserved.

Research Area(s)

  • Concavity, Non-crossing, Production frontier, Productivity and competitiveness, Quantile regression, Shape restriction

Citation Format(s)