A penalized method for multivariate concave least squares with application to productivity analysis
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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.
|Number of pages||14|
|Journal||European Journal of Operational Research|
|Publication status||Published - 16 Mar 2017|
|MoE publication type||A1 Journal article-refereed|
- Concave regression, Convex regression, Penalization method, Production function