Robust nonparametric frontier estimators: Qualitative robustness and influence function

Statistica Sinica

Volumn 16, Issue 4, 2006, Pages 1233-1253

  Daouia, Abdelaati ^a,b   Ruiz Gazen, Anne ^a,c  

^a UNIVERSITÉ DE TOULOUSE   (France)

^b INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^c TOULOUSE SCHOOL OF ECONOMICS   (France)

Author keywords

Estimation of a monotone boundary; Gross error sensitivity; Influence function; Maximum bias; Outliers detection; Productivity analysis; Prohorov distance; Qualitative robustness

Indexed keywords

EID: 33846554899     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. Aragon, Y., Daouia, A. and Thomas-Agnan, C. (2005). Nonparametric frontier estimation: a conditional quantile-based approach. Econom. Theory 21, 358-389.
2. Banker, R. D. (1993). Maximum likelihood, consistency and data envelopment analysis: a statistical foundation. Management Sci. 39, 1265-1273.
3. Cazals, C., Florens, J-P. and Simar, L. (2002). Nonparametric frontier estimation: a robust approach. J. Econometrics 106, 1-25.
4. Daouia, A. and Ruiz-Gazen, A. (2004), Robust nonparametric frontier estimators: qualitative robustness and influence function. Technical report, GREMAQ et LSP, Université de Toulouse (http://w3.univ-tlse1.fr/GREMAQ/ Statistique/ar0903.pdf).
5. Deprins, D., Simar, L. and Tulkens, H. (1984). Measuring labor efficiency in post offices. In The Performance of Public Enterprises: Concepts and Measurements (Edited by M. Marchand, P. Pestieau and H. Tulkens), 243-267, North-Holland, Amsterdam.
6. Farrell, M. J. (1957). The measurement of productive efficiency. J. Roy. Statist. Soc. Ser. A 120, 253-281.
7. Florens, J-P. and Simar, L. (2005). Parametric approximations of nonparametric frontiers. J. Econometrics 124, 91-116.
8. Gijbels, I., Mammen, E., Park, B. U. and Simar, L. (1999). On estimation of monotone and concave frontier functions. J. Amer. Statist. Assoc. 94, 220-228.
9. Greene, W. H. (1980). Maximum likelihood estimation of econometric frontier functions. J. Econometrics 13, 27-56.
10. Hampel, F. R. (1971). A general qualitative definition of robustness. Ann. Math. Statist. 42, 1887-1896.
11. Hampel, F. R. (1974). The influence curve and its role in robust estimation. J. Amer. Statist. Assoc. 69, 383-393.
12. Hampel, F. R., Ronchetti, E. M. and Rousseeuw, P. J. and Stahel, W. A. (1986). Robust Statistics: The Approach Based on Influence Functions. Wiley, New York.
13. Huber, P. J. (1981). Robust Statistics. Wiley, New York.
14. Korostelev, A., Simar, L. and Tsybakov, A. B. (1995). Efficient estimation of monotone boundaries. Ann. Statist. 23, 476-489.
15. Markovitz, H. M. (1959). Portfolio Selection: Efficient Diversification of Investments. Wiley, New York.
16. Park, B. U., Simar, L. and Weiner, C. (2000). The FDH estimator for productivity efficiency scores. Econom. Theory 16, 855-877.
17. Prohorov, Y. V. (1956). Convergence of random processes and limit theorems in probability theory. Theory Probab. Appl. 1, 157-214.
18. Rousseeuw, P. J. (1981). A new infinitesimal approach to robust estimation. Z. Wahrsch. Verw. Gebiete 56, 127-132.
19. Seiford, L. M. (1996). Data Envelopment Analysis: The Evolution of the State-of-the-Art (1978-1995). J. Productiv. Anal. 7, 99-138.
20. Simar, L. (2003). Detecting Outliers in Frontier Models: A Simple Approach. J. Productiv. Anal. 20, 391-424.
21. Van der Vaart, A. W. (1998). Asymptotic Statistics. Cambridge University Press.