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

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A penalized method for multivariate concave least squares with application to productivity analysis. / Keshvari, Abolfazl.

In: European Journal of Operational Research, Vol. 257, No. 3, 16.03.2017, p. 1016-1029.

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@article{f53768808b8a4c79a5d456abd96644f2,
title = "A penalized method for multivariate concave least squares with application to productivity analysis",
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.",
keywords = "Concave regression, Convex regression, Penalization method, Production function",
author = "Abolfazl Keshvari",
year = "2017",
month = "3",
day = "16",
doi = "10.1016/j.ejor.2016.08.026",
language = "English",
volume = "257",
pages = "1016--1029",
journal = "European Journal of Operational Research",
issn = "0377-2217",
publisher = "Elsevier Science B.V.",
number = "3",

}

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TY - JOUR

T1 - A penalized method for multivariate concave least squares with application to productivity analysis

AU - Keshvari, Abolfazl

PY - 2017/3/16

Y1 - 2017/3/16

N2 - 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.

AB - 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.

KW - Concave regression

KW - Convex regression

KW - Penalization method

KW - Production function

UR - http://www.scopus.com/inward/record.url?scp=84994176301&partnerID=8YFLogxK

U2 - 10.1016/j.ejor.2016.08.026

DO - 10.1016/j.ejor.2016.08.026

M3 - Article

VL - 257

SP - 1016

EP - 1029

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 3

ER -

ID: 11703191