Inference by the m out of n bootstrap in nonparametric frontier models

Journal of Productivity Analysis

Volumn 36, Issue 1, 2011, Pages 33-53

  Simar, Léopold ^a,b   Wilson, Paul W ^c  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b Toulouse School of Economics   (France)

^c Bowling Green State University   (United States)

Author keywords

Bootstrap; Efficiency; Nonparametric frontier; Nonparametric testing; Testing convexity; Testing returns to scale

Indexed keywords

EID: 79960060758     PISSN: 0895562X     EISSN: 15730441     Source Type: Journal    
DOI: 10.1007/s11123-010-0200-4     Document Type: Article

References (45)

1. Banker RD (1993) Maximum likelihood, consistency and data envelopment analysis: a statistical foundation. Manag Sci 39: 1265-1273.
2. Banker RD (1996) Hypothesis tests using data envelopment analysis. J Prod Anal 7: 139-159.
3. Beran R, Ducharme G (1991) Asymptotic theory for bootstrap methods in statistics. Centre de Reserches Mathematiques, University of Montreal, Montreal.
4. Bickel PJ, Freedman DA (1981) Some asymptotic theory for the bootstrap. Ann Stat 9: 1196-1217.
5. Bickel PJ, Sakov A (2008) On the choice of m in the m out of n bootstrap and confidence bounds for extrema. Stat Sin 18: 967-985.
6. Bretagnolle J (1983) Lois limites du bootstrap des certaines fonctionnelles. Ann Inst Henri Poincare (Sect B) 19: 223-234.
7. Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Resarch 2: 429-444.
8. Charnes A, Cooper WW, Rhodes E (1979) Measuring the efficiency of decision making units. Eur J Oper Res 3: 339.
9. Debreu G (1951) The coefficient of resource utilization. Econometrica 19: 273-292.
10. Deprins D, Simar L, Tulkens H (1984) Measuring labor inefficiency in post offices. In: Pestieau MMP, Tulkens H (eds) The performance of public enterprises: concepts and measurements. North-Holland, Amsterdam, pp 243-267.
11. Efron B (1979) Bootstrap methods: another look at the jackknife. Ann Stat 7: 1-16.
12. Färe R (1988) Fundamentals of production theory. Springer, Berlin.
13. Färe R, Grosskopf S, Lovell CAK (1985) The measurement of efficiency of production. Kluwer-Nijhoff Publishing, Boston.
14. Farrell MJ (1957) The measurement of productive efficiency. J R Stat Soc A 120: 253-281.
15. Gijbels I, Mammen E, Park BU, Simar L (1999) On estimation of monotone and concave frontier functions. J Am Stat Assoc 94: 220-228.
16. Härdle W, Mammen E (1993) Comparing nonparametric versus parametric regression fits. Ann Stat 21: 1926-1947.
17. Jeong SO (2004) Asymptotic distribution of DEA efficiency scores. J Korean Stat Soc 33: 449-458.
18. Jeong SO, Simar L (2006) Linearly interpolated FDH efficiency score for nonconvex frontiers. J Multivar Anal 97: 2141-2161.
19. Kittelsen SAC (1999) Monte Carlo simulations of DEA efficiency measures and hypothesis tests. Unpublished working paper, memorandum no. 09/99, Department of Economics, University of Oslo, Norway.
20. Kneip A, Park B, Simar L (1998) A note on the convergence of nonparametric DEA efficiency measures. Econom Theory 14: 783-793.
21. Kneip A, Simar L, Wilson PW (2008) Asymptotics and consistent bootstraps for DEA estimators in non-parametric frontier models. Econom Theory 24: 1663-1697.
22. Kneip A, Simar L, Wilson PW (2010) A computationally efficient, consistent bootstrap for inference with non-parametric DEA estimators. Comput Econ (forthcoming)
23. Korostelev A, Simar L, Tsybakov AB (1995a) Efficient estimation of monotone boundaries. Ann Stat 23: 476-489.
24. Korostelev A, Simar L, Tsybakov AB (1995b) On estimation of monotone and convex boundaries. Publ Inst Stat Univ Paris XXXIX 1: 3-18.
25. Mammen E (1992) When does bootstrap work? Asymptotic results and simulations. Springer, Berlin.
26. Park BU, Simar L, Weiner C (2000) FDH efficiency scores from a stochastic point of view. Econom Theory 16: 855-877.
27. Park BU, Jeong S-O, Simar L (2010) Asymptotic distribution of conical-hull estimators of directional edges. Ann Stat 38: 1320-1340.
28. Politis DN, Romano JP (1994) Large sample confidence regions based on subsamples under minimal assumtions. Ann Stat 22: 2031-2050.
29. Politis DN, Romano JP (1999) Subsampling. Springer, New York.
30. Politis DN, Romano JP, Wolf M (2001) On the asymptotic theory of subsampling. Stat Sin 11: 1105-1124.
31. Serfling RJ (1980) Approximation theorems of mathematical statistics. Wiley, New York.
32. Shephard RW (1970) Theory of cost and production functions. Princeton University Press, Princeton.
33. Simar L (1996) Aspects of statistical analysis in DEA-type frontier models. J Prod Anal 7: 177-185.
34. Simar L, Wilson PW (1998) Sensitivity analysis of efficiency scores: how to bootstrap in nonparametric frontier models. Manag Sci 44: 49-61.
35. Simar L, Wilson PW (1999a) Some problems with the Ferrier/Hirschberg bootstrap idea. J Prod Anal 11: 67-80.
36. Simar L, Wilson PW (1999b) Of course we can bootstrap DEA scores! But does it mean anything? Logic trumps wishful thinking. J Prod Anal 11: 93-97.
37. Simar L, Wilson PW (2000a) A general methodology for bootstrapping in non-parametric frontier models. J Appl Stat 27: 779-802.
38. Simar L, Wilson PW (2000b) Statistical inference in nonparametric frontier models: the state of the art. J Prod Anal 13: 49-78.
39. Simar L, Wilson PW (2001a) Nonparametric tests of returns to scale. Eur J Oper Res 139: 115-132.
40. Simar L, Wilson PW (2001b) Testing restrictions in nonparametric efficiency models. Commun Stat 30: 159-184.
41. Swanepoel JWH (1986) A note on proving that the (modified) bootstrap works. Commun Stat Theory Methods 15: 3193-3203.
42. van der Vaart AW (2000) Asymptotic statistics. Cambridge University Press, Cambridge.
43. Wheelock DC, Wilson PW (2008) Non-parametric, unconditional quantile estimation for efficiency analysis with an application to Federal Reserve check processing operations. J Econom 145: 209-225.
44. Wilson PW (2008) FEAR: a software package for frontier efficiency analysis with R. Socio Econ Plan Sci 42: 247-254.
45. Wilson PW (2010) Asymptotic properties of some non-parametric hyperbolic efficiency estimators. In: van Keilegom I, Wilson PW (eds) Exploring research frontiers in contemporary statistics and econometrics. Physica-Verlag, Berlin (forthcoming).