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Aspects of statistical analysis in DEA-type frontier models

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Simar, Léopold [UCL]

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 process 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.

Document type Communication à un colloque (Conference Paper) – Présentation orale avec comité de sélection
Access type Accès restreint
Publication date 1996
Language Anglais
Conference "Advanced Workshop on Efficiency Measurement", ODENSE UNIV, ODENSE (Denmark) (May 22-24, 1995)
Journal information "Journal of Productivity Analysis" - Vol. 7, no. 2-3, p. 177-185 (1996)
Peer reviewed yes
issn 0895-562X
e-issn 1573-0441
Publisher Kluwer Academic Publ (Dordrecht)
Affiliations UCL - EUEN/CORE - Center for operations research and econometrics
UCL - EUEN/STAT - Institut de statistique
Keywords Statistical Analysis ; Dea Frontier Models ; Bootstrap
Links
  1. Aigner, D.J., C.A.K. Lovell, and P. Schmidt. (1977). ?Formulation and Estimation of Stochastic Frontier Models.? Journal of Econometrics 6, 21?37.
  2. Banker, R.D. (1993). ?Maximum Likelihood, Consistency and Data Envrlopment Analysis: A Statistical Foundation.? Management Science 39, 10, 1265?1273.
  3. Banker, R.D. (1995). ?Hypothesis Testing Using Data Envelopment Analysis.? Paper presented at the Advanced Research Workshop on Efficiency Measurement, Odense University, May 22?24, 1995.
  4. Charnes, A., W.W. Cooper, and E. Rhodes. (1978). ?Measuring the Inefficiency of Decision Making Units.? European Journal of Operational Research 2, 429?444.
  5. Deprins, D., L. Simar, and H. Tulkens. (1984). ?Measuring Labor Inefficiency in Post Offices.? In M. Marchand, P. Pestieau, and H. Tulkens (eds.), The Performance of Public Enterprises: Concepts and Measurements. Amsterdam: North-Holland.
  6. Fan, J., T.C. Hu, and Y.K. Truong. (1994). ?Robust Non-Parametric Function Estimation.? The Scandinavian Journal of Statistics 21, 433?446.
  7. Farrell, M.J. (1957). ?The Measurement of Productive Efficiency.? Journal of the Royal Statistical Society A(120), 253?281.
  8. Greene, W.H. (1980). ?Maximum Likelihood Estimation of Econometric Frontier.? Journal of Econometrics 13, 27?56.
  9. Grosskopf, S. (1995). ?Statistical Inference and Nonnparametric Efficiency: A Selective Survey.? Paper presented at the Advanced Research Workshop on Efficiency Measurement, Odense University, May 22?24, 1995.
  10. Kittelsen, S.A.C. (1995). ?Monte Carlo Simulations of DEA Efficiency Measures and Hypothesis Tests.? In Using Data Envelopment Analysis to Measure Production Efficiency in the Public Sector. Thesis for the degree of Dr. Polit, at the Department of Economics, University of Oslo.
  11. Kneip, A. and L. Simar. (1995). ?A General Framework for Frontier Estimation with Panel Data.? Paper presented at the Advanced Research Workshop on Efficiency Measurement, Odense University, May 22?24, 1995.
  12. Korostelev, A., L. Simar, and A. Tsybakov. (1995a). ?Efficient Estimation of Monotone Boundaries.? The Annals of Statistics 23(2), 476?489.
  13. Korostelev, A., L. Simar, and A. Tsybakov. (1995b). ?On Estimation of Monotone and Convex Boundaries.? Pub. Inst. Stat. Univ. Paris XXXIX, 1, 3?18.
  14. Simar, L. (1992). ?Estimating Efficiencies from Frontier Models with Panel Data: A Comparison of Parametric, Non-Parametric and Semi-Parametric Methods with Bootstrapping.? Journal of Producivity Analysis 3, 167?203.
  15. Simar, L. and P.W. Wilson. (1995). ?Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models.? Discussion paper 9503, Institut de Statistique, UCL, Louvain-la-Neuve, Belgium, to appear in Management Sciences.
  16. Thiry, B. and H. Tulkens. (1992). ?Allowing for Technical Inefficiency in Parametric Estimates of Production Functions.? Journal of Productivity Analysis 3, 41?62.
  17. Wilson, P.W. and L. Simar. (1995). ?Bootstrap Estimation for Nonparametric Efficiency Estimates.? Discussion paper 9517, Institut de Statistique, UCL, Louvain-la-Neuve, Belgium.
  18. Wilson, P.W. and L. Simar. (1996). ?Nonparametric Tests of Returns to Scale.? Forthcoming manuscript.
Bibliographic reference Simar, Léopold. Aspects of statistical analysis in DEA-type frontier models.Advanced Workshop on Efficiency Measurement (ODENSE UNIV, ODENSE (Denmark), May 22-24, 1995). In: Journal of Productivity Analysis, Vol. 7, no. 2-3, p. 177-185 (1996)
Permanent URL http://hdl.handle.net/2078.1/62987