A More Efficient Algorithm for Convex Nonparametric Least Squares

European Journal of Operational Research, 227 (2), 391-400

28 Pages Posted: 8 Jan 2012 Last revised: 19 Jul 2013

See all articles by Chia-Yen Lee

Chia-Yen Lee

National Cheng Kung University

Andrew L Johnson

Texas A&M University

Erick Moreno-Centeno

Texas A&M University

Timo Kuosmanen

Aalto University School of Business

Date Written: December 1, 2011

Abstract

Convex Nonparametric Least Squares (CNLS) is a nonparametric regression method that does not require a priori specification of the functional form. The CNLS problem is solved by mathematical programming techniques; however, since the CNLS problem size grows quadratically as a function of the number of observations, standard Quadratic Programming (QP) and Nonlinear Programming (NLP) algorithms are inadequate for handling large samples, and the computational burdens become significant even for relatively small samples. This study proposes a generic algorithm that improves the computational performance in small samples and is able to solve problems that are currently unattainable. A Monte Carlo simulation is performed to evaluate the performance of six variants of the proposed algorithm. These experimental results indicate that a particular variant is most efficient given the sample size and the dimensionality. The computational benefits of the new algorithm are demonstrated by an empirical application that proved insurmountable for the standard QP and NLP algorithms.

Keywords: Convex Nonparametric Least Squares, Frontier Estimation, Productive Efficiency Analysis, Model Reduction, Computational Complexity

Suggested Citation

Lee, Chia-Yen and Johnson, Andrew L and Moreno-Centeno, Erick and Kuosmanen, Timo, A More Efficient Algorithm for Convex Nonparametric Least Squares (December 1, 2011). European Journal of Operational Research, 227 (2), 391-400. Available at SSRN: https://ssrn.com/abstract=1981260 or http://dx.doi.org/10.2139/ssrn.1981260

Chia-Yen Lee

National Cheng Kung University ( email )

No.1, University Road
Tainan
Taiwan

Andrew L Johnson (Contact Author)

Texas A&M University ( email )

4033 Emerging Technologies Building
College Station, Texas 77843-3131
College Station, TX 77843-4353
United States

HOME PAGE: http://www.andyjohnson.guru

Erick Moreno-Centeno

Texas A&M University ( email )

College Station, TX 77843-4353
United States

Timo Kuosmanen

Aalto University School of Business ( email )

P.O. Box 1210
Runeberginkatu 22-24
Helsinki, Finland 00101
Finland

HOME PAGE: http://www.aalto.fi

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