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P.W. Wilson (1995), “Detecting Influential Observations in Data Envelopment Analysis,” Journal of Productivity Analysis 6, pp.27–46.
See, for instance, R.M. Thrall (1989), “Classification of Transitions under Expansion of Inputs and Outputs,” Managerial and Decision Economics 10, pp.159–162.
R.D. Banker, H. Chang and W.W. Cooper (1996), “Simulation Studies of Efficiency, Returns to Scale and Misspecification with Nonlinear Functions in DEA,” Annals of Operations Research 66, pp.233–253.
A. Charnes, W.W. Cooper, A.Y. Lewin, R.C. Morey and J.J. Rousseau (1985), “Sensitivity and Stability Analysis in DEA,” Annals of Operations Research 2, pp.139–156.
A. Charnes and W.W. Cooper (1968), “Structural Sensitivity Analysis in Linear Programming and an Exact Product Form Left Inverse,” Naval Research Logistics Quarterly 15, pp.517–522.
For a summary discussion see A. Charnes and L. Neralic (1992), “Sensitivity Analysis in Data Envelopment Analysis 3,” Glasnik Matematicki 27, pp.191–201. A subsequent extension is L. Neralic (1997), “Sensitivity in Data Envelopment Analysis for Arbitrary Perturbations of Data,” Glasnik Matematicki 32, pp.315–335. See also L. Neralic (2004), “Preservation of Efficiency and Inefficiency Classification in Data Envelopment Analysis,” Mathematical Communications 9, pp.51–62.
A. Charnes, S. Haag, P. Jaska and J. Semple (1992), “Sensitivity of Efficiency Calculations in the Additive Model of Data Envelopment Analysis,” International Journal of System Sciences 23, pp.789–798. Extensions to other classes of models may be found in A. Charnes, J.J. Rousseau and J.H.Semple (1996) “Sensitivity and Stability of Efficiency Classifications in DEA,” Journal of Productivity Analysis 7, pp.5–18.
The shape of this “ball” will depend on the norm that is used. For a discussion of these and other metric concepts and their associated geometric portrayals see Appendix A in A. Charnes and W.W. Cooper (1961), Management Models and Industrial Applications of Linear Programming (New York: John Wiley & Sons).
This omission of DMUo is also used in developing a measure of “super efficiency” as it is called in P. Andersen and N.C. Petersen (1993), “A Procedure for Ranking Efficient Units in DEA,” Management Science 39, pp.1261–1264. Their use is more closely associated with stability when a DMU is omitted, however, so we do not cover it here. See the next chapter, Chapter 10, in this text. See also R.M. Thrall (1996) “Duality Classification and Slacks in DEA,” Annals of Operations Research 66, pp.104–138.
A. Charnes, J.J. Rousseau and J.H. Semple (1996), “Sensitivity and Stability of Efficiency Classification in Data Envelopment Analysis,” Journal of Productivity Analysis 7, pp.5–18.
In fact, Seiford and Zhu propose an iterative approach to assemble an exact stability region in L. Seiford and J. Zhu, “Stability Regions for Maintaining Efficiency in Data Envelopment Analysis,” European Journal of Operational Research 108, 1998, pp.127–139.
R.G. Thompson, P.S. Dharmapala and R.M. Thrall (1994), “Sensitivity Analysis of Efficiency Measures with Applications to Kansas Farming and Illinois Coal Mining,” in A. Charnes, W.W. Cooper, A.Y. Lewin and L.M. Seiford, eds., Data Envelopment Analysis: Theory, Methodology and Applications (Norwell, Mass., Kluwer Academic Publishers) pp.393–422.
R.G. Thompson, P.S. Dharmapala, J. Diaz, M.D. Gonzales-Lina and R.M. Thrall (1996), “DEA Multiplier Analytic Center Sensitivity Analysis with an Illustrative Application to Independent Oil Cos.,” Annals of Operations Research 66, pp.163–180.
A. Charnes, W.W. Cooper and R.M. Thrall (1991), “A Structure for Classifying and Characterizing Efficiency in Data Envelopment Analysis,” Journal of Productivity Analysis 2, pp.197–237.
An alternate approach to simultaneous variations in all data effected by the envelopment model is available in L.M. Seiford and J. Zhu (1998), “Sensitivity Analysis of DEA Models for Simultaneous Changes in All Data,” Journal of the Operational Research Society 49, pp.1060–1071. See also the treatments of simultaneous changes in all data for additive models in L. Neralic (2004), “Preservation of Efficiency and Inefficiency Classification in Data Envelopment Analysis,” Mathematical Communications 9, pp.51–62.
This status is easily recognized because θ1* = θ2* = θ3* = 1 are all associated with uniquely obtained solutions with zero slacks. See A. Charnes, W.W. Cooper and R.M. Thrall (1991) “A Structure for Classifying and Characterizing Efficiency in Data Envelopment Analysis,” Journal of Productivity Analysis 2, pp.197–237.
W.W. Cooper, S. Li, L.M. Seiford and J. Zhu (2004), Chapter 3 in W.W. Cooper, L.M. Seiford and J. Zhu, eds., Handbook on Data Envelopment Analysis (Norwell, Mass., Kluwer Academic Publishers).
R.D. Banker (1993), “Maximum Likelihood, Consistency and Data Envelopment Analysis: A Statistical Foundation,” Management Science 39, pp.1265–1273.
R. Banker and R. Natarasan (2004), “Statistical Tests Based on DEA Efficiency Scores,” Chapter 11 in in W.W. Cooper, L.M. Seiford and J. Zhu, eds., Handbook on Data Envelopment Analysis (Norwell, Mass., Kluwer Academic Publishers).
Quoted from p.139 in R.D Banker (1996), “Hypothesis Tests Using Data Envelopment Analysis,” Journal of Productivity Analysis pp.139–159.
A.P. Korostolev, L. Simar and A.B. Tsybakov (1995), “On Estimation of Monotone and Convex Boundaries,” Public Institute of Statistics of the University of Paris, pp.3–15. See also Korostolev, Simar and Tsybakov (1995), “Efficient Estimation of Monotone Boundaries,” Annals of Statistics 23, pp.476–489.
See the discussion in L. Simar (1996), “Aspects of Statistical Analysis in DEA-Type Frontier Models,” Journal of Productivity Analysis 7, pp.177–186.
L. Simar and P.W. Wilson (1998), “Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models,” Management Science 44, pp.49–61. See also Simar and Wilson (2004) “Performance of the Bootstrap for DEA Estimators and Iterating the Principle,” Chapter 10 in W.W. Cooper, L.M. Seiford and J. Zhu, eds. Handbook on Data Envelopment Analysis (Norwell, Mass: Kluwer Academic Publishers).
M.J. Farrell (1951), “The Measurement of Productive Efficiency,” Journal of the Royal Statistical Society Series A, 120, pp.253–290.
D.J. Aigner and S.F. Chu (1968), “On Estimating the Industry Production Frontiers,” American Economic Review 56, pp.826–839.
D.J. Aigner, C.A.K. Lovell and P. Schmidt (1977), “Formulation and Estimation of Stochastic Frontier Production Models,” Journal of Econometrics 6, pp.21–37. See also W. Meeusen and J. van den Broeck (1977) “Efficiency Estimation from Cobb-Douglas Functions with Composed Error,” International Economic Review 18, pp.435–444.
J. Jondrow, C.A.K. Lovell, I.S. Materov and P. Schmidt (1982), “On the Estimation of Technical Inefficiency in the Stochastic Frontier Production Model,” Journal of Econometrics 51, pp.259–284.
B.H. Gong and R.C. Sickles (1990), “Finite Sample Evidence on the Performance of Stochastic Frontiers and Data Envelopment Analysis Using Panel Data,” Journal of Econometrics 51, pp.259–284.
P. Schmidt (1985–1986), “Frontier Production Functions,” Econometric Reviews 4, pp.289–328. See also P.W. Bauer (1990), “Recent Development in Econometric Estimation of Frontiers,” Journal of Econometrics 46, pp.39–56.
G.D. Ferrier and C.A.K. Lovell (1990), “Measuring Cost Efficiency in Banking — Econometric and Linear Programming Evidence,” Journal of Econometrics 6, pp.229–245.
A. Charnes, W.W. Cooper and T. Sueyoshi (1988), “A Goal Programming/Constrained Regression Review of the Bell System Breakup,” Management Science 34, pp.1–26.
See R.S. Barr, L.M. Seiford and T.F. Siems (1994), “Forcasting Bank Failure: A Non-Parametric Frontier Estimation Approach,” Recherches Economiques de Louvain 60, pp. 417–429. for an example of a different two-stage DEA regression approach in which the DEA scores from the first stage served as an independent variable in the second stage regression model.
V. Arnold, I.R. Bardhan, W.W. Cooper and S.C. Kumbhakar (1994), “New Uses of DEA and Statistical Regressions for Efficiency Evaluation and Estimation — With an Illustrative Application to Public Secondary Schools in Texas,” Annals of Operations Research 66, pp.255–278.
I.R. Bardhan, W.W. Cooper and S.C. Kumbhakar (1998), “A Simulation Study of Joint Uses of Data Envelopment Analysis and Stochastic Regressions for Production Function Estimation and Efficiency Evaluation,” Journal of Productivity Analysis 9, pp.249–278.
P.L. Brockett, W.W. Cooper, S.C. Kumbhakar, M.J. Kwinn Jr. and D. McCarthy (2004), “Alternative Statistical Regression Studies of the Effects of Joint and Service-Specific Advertising on Military Recruitment,” Journal of the Operational Research Society 55, pp.1039–1048.
S. Thore (1987), “Chance-Constrained Activity Analysis,” European Journal of Operational Research 30, pp.267–269.
See the following three papers by K.C. Land, C.A.K. Lovell and S. Thore: (1) “Productive Efficiency under Capitalism and State Socialism: the Chance Constrained Programming Approach” in Pierre Pestieau, ed. in Public Finance in a World of Transition (1992) supplement to Public Finance 47, pp.109–121; (2) “Chance-Constrained Data Envelopment Analysis,” Managerial and Decision Economics 14, 1993, pp.541–554; (3) “Productive Efficiency under Capitalism and State Socialism: An Empirical Inquiry Using Chance-Constrained Data Envelopment Analysis,” Technological Forecasting and Social Change 46, 1994, pp.139–152. In “Four Papers on Capitalism and State Socialism” (Austin Texas: The University of Texas, IC2 Institute) S. Thore notes that publication of (2) was delayed because it was to be presented at a 1991 conference in Leningrad which was cancelled because of the Soviet Crisis.
W.W. Cooper, Z. Huang and S. Li (1996), “Satisficing DEA Models under Chance Constraints,” Annals of Operations Research 66, pp.279–295. For a survey of chance constraint programming uses in DEA, see W.W. Cooper, Z. Huang and S. Li (2004), “Chance Constraint DEA,” in W.W. Cooper, R.M. Seiford and J. Zhu, eds., Handbook on Data Envelopment Analysis (Norwell, Mass., Kluwer Academic Publishers).
See Chapter 15 in H.A. Simon (1957), Models of Man (New York: John Wiley & Sons, Inc.)
A. Charnes and W.W. Cooper (1963), “Deterministic Equivalents for Optimizing and Satisficing under Chance Constraints,” Operations Research 11, pp.18–39.
See W.F. Sharpe (1970), Portfolio Theory and Capital Markets (New York: McGraw Hill, Inc.)
O.B. Olesen and N.C. Petersen (1995), “Chance Constrained Efficiency Evaluation,” Management Science 41, pp.442–457.
W.W. Cooper, Z. Huang, S.X. Li and O.B. Olesen (1998), “Chance Constrained Programming Formulations for Stochastic Characterizations of Efficiency and Dominance in DEA,” Journal of Productivity Analysis 9, pp.53–79.
See A. Charnes and W.W. Cooper (1963) in footnote 41, above.
A. Charnes, W.W. Cooper and G.H. Symods (1958), “Cost Horizons and Certainty Equivalents,” Management Science 4, pp.235–263.
G. Gigerenzer (2004), “Striking a Blow for Sanity in Theories of Rationality,” in M. Augier and J.G. March, eds., Models of a Man: Essays in Memory of H.A. Simon (Cambridge: MIT Press).
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Cooper, W.W., Seiford, L.M., Tone, K. (2007). Data Variations. In: Data Envelopment Analysis. Springer, New York, NY. https://doi.org/10.1007/978-0-387-45283-8_9
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