Data Envelopment Analysis as Nonparametric Least Squares Regression

Kuosmanen, T. and A.L. Johnson, 2010. “Data Envelopment Analysis as Nonparametric Least Squares Regression.” Operations Research 58(1): 149-160.

30 Pages Posted: 11 Jul 2008 Last revised: 23 Feb 2018

Timo Kuosmanen

Aalto University School of Business

Andrew L Johnson

Texas A&M University

Date Written: July 11, 2008

Abstract

Data Envelopment Analysis (DEA), a nonparametric mathematical programming approach to productive efficiency analysis, envelops all observed data. In this paper we show that DEA can be interpreted as nonparametric least squares regression subject to shape constraints on frontier and sign constraints on residuals, and that classic parametric programming model is a constrained special case of DEA. Applying these insights, we present a nonparametric variant of the corrected ordinary least squares (COLS) method. We show that this new method, which we term corrected concave nonparametric least squares (C2NLS) is consistent and asymptotically unbiased. The linkages established in this paper contribute to further integration of the econometric and linear programming approaches.

Keywords: frontier estimation, nonparametric regression, parametric programming, performance measurement and benchmarking, productive efficiency analysis, data envelopment analysis

Suggested Citation

Kuosmanen, Timo and Johnson, Andrew L, Data Envelopment Analysis as Nonparametric Least Squares Regression (July 11, 2008). Kuosmanen, T. and A.L. Johnson, 2010. “Data Envelopment Analysis as Nonparametric Least Squares Regression.” Operations Research 58(1): 149-160. . Available at SSRN: https://ssrn.com/abstract=1158252 or http://dx.doi.org/10.2139/ssrn.1158252

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

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

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