A penalized method for multivariate concave least squares with application to productivity analysis

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  • Abolfazl Keshvari

Research units


We propose a penalized method for the least squares estimator of a multivariate concave regression function. This estimator is formulated as a quadratic programing (QP) problem with O(n2) constraints, where n is the number of observations. Computing such an estimator is a very time-consuming task, and the computational burden rises dramatically as the number of observations increases. By introducing a quadratic penalty function, we reformulate the concave least squares estimator as a QP with only non-negativity constraints. This reformulation can be adapted for estimating variants of shape restricted least squares, i.e. the monotonic-concave/convex least squares. The experimental results and an empirical study show that the reformulated problem and its dual are solved significantly faster than the original problem. The Matlab and R codes for implementing the penalized problems are provided in the paper.


Original languageEnglish
Pages (from-to)1016-1029
Number of pages14
JournalEuropean Journal of Operational Research
Issue number3
Publication statusPublished - 16 Mar 2017
MoE publication typeA1 Journal article-refereed

    Research areas

  • Concave regression, Convex regression, Penalization method, Production function

ID: 11703191