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

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  • Keshvari, Abolfazl

Abstract

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.

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  • Keshvari, Abolfazl, 2017. "A penalized method for multivariate concave least squares with application to productivity analysis," European Journal of Operational Research, Elsevier, vol. 257(3), pages 1016-1029.
    • Handle: RePEc:eee:ejores:v:257:y:2017:i:3:p:1016-1029
    DOI: 10.1016/j.ejor.2016.08.026
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    3. Zhiqiang Liao, 2024. "Variable selection in convex nonparametric least squares via structured Lasso: An application to the Swedish electricity distribution networks," Papers 2409.01911, arXiv.org, revised Nov 2024.

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