Aspects of statistical analysis in DEA-type frontier models

In Grosskopf (1995) and Banker (1995) different approaches and problems of statistical inference in DEA frontier models are presented. This paper focuses on the basic characteristics of DEA models from a statistical point of view. It arose from comments and discussions on both papers above. The framework of DEA models is deterministic (all the observed points lie on the same side of the frontier), nevertheless a stochastic model can be constructed once a data generating process is defined. So statistical analysis may be performed and sampling properties of DEA estimators can be established. However, practical statistical inference (such as test of hypothesis, confidence intervals) still needs artifacts like the bootstrap to be performed. A consistent bootstrap relies also on a clear definition of the data generating proces and on a consistent estimator of it: The approach of Simar and Wilson (1995) is described. Finally, some trails are proposed for introducing stochastic noise in DEA models, in the spirit of the Kneip-Simar (1995) approach.

[1]  Jianqing Fan,et al.  Robust Non-parametric Function Estimation , 1994 .

[2]  Bernard Thiry,et al.  Allowing for inefficiency in parametric estimation of production functions for urban transit firms , 1992 .

[3]  D. Aigner,et al.  P. Schmidt, 1977,?Formulation and estimation of stochastic frontier production function models,? , 1977 .

[4]  R. Banker.  Maximum likelihood, consistency and data envelopment analysis: a statistical foundation , 1993 .

[5]  W. Greene.  Maximum likelihood estimation of econometric frontier functions , 1980 .

[6]  Léopold Simar,et al.  Estimating efficiencies from frontier models with panel data: A comparison of parametric, non-parametric and semi-parametric methods with bootstrapping , 1992 .

[7]  Léopold Simar,et al.  A general framework for frontier estimation with panel data , 1996 .

[8]  M. Farrell.  The Measurement of Productive Efficiency , 1957 .

[9]  A. Tsybakov,et al.  Efficient Estimation of Monotone Boundaries , 1995 .

[10]  P. W. Wilson,et al.  Bootstrap Estimation for Nonparametric Efficiency Estimates , 1995 .

[11]  S. Grosskopf.  Statistical inference and nonparametric efficiency: A selective survey , 1996 .

[12]  P. W. Wilson,et al.  Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models , 1998 .

[13]  Abraham Charnes,et al.  Measuring the efficiency of decision making units , 1978 .

[14]  Léopold Simar,et al.  On estimation of monotone and convex boundaries , 1995 .

[15]  Dieter Gstach.  A new approach to stochastic frontier estimation: DEA+ , 1996 .