Estimation and inference in nonparametric frontier models: Recent developments and perspectives

Foundations and Trends in Econometrics

Volumn 5, Issue 3-4, 2011, Pages 183-337

  Simar, Leopold ^a   Wilson, Paul W ^b  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b CLEMSON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84880898875     PISSN: 15513076     EISSN: 15513084     Source Type: Journal    
DOI: 10.1561/0800000020     Document Type: Review

References (119)

1. Aigner, D., C. A. K. Lovell, and P. Schmidt (1977), 'Formulation and estimation of stochastic frontier production function models'. Journal of Econometrics 6, 21-37.
2. Aragon, Y., A. Daouia, and C. Thomas-Agnan (2005), 'Nonparametric frontier estimation: A conditional quantile-based approach'. Econometric Theory 21, 358-389. (Pubitemid 40551427)
3. Athreya, B. K. (1987), 'Bootstrap of the mean in the infinite variance case'. Annals of Statistics 15, 724-731.
4. Banker, D. R. (1993), 'Maximum likelihood, consistency and data envelopment analysis: A statistical foundation'. Management Science 39, 1265-1273.
5. Banker, D. R., A. Charnes, and W. W. Cooper (1984), 'Some models for estimating technical and scale inefficiencies in data envelopment analysis'. Management Science 30, 1078-1092. (Pubitemid 14651320)
6. Banker, D. R. and R. Natarajan (2008), 'Evaluating contextual variables affecting productivity using data envelopment analysis'. Operations Research 56, 48-58. (Pubitemid 351463108)
7. Battese, E. G. and G. S. Corra (1977), 'Estimation of a production frontier model: With application to the pastoral zone off eastern Australia'. Australian Journal of Agricultural Economics 21, 169-179.
8. Beran, R. and G. Ducharme (1991), Asymptotic Theory for Bootstrap Methods in Statistics. Montreal: Centre de Reserches Mathematiques, University of Montreal.
9. Beran, R. and M. S. Srivastava (1985), 'Bootstrap tests and confidence regions for functions of a covariance matrix'. Annals of Statistics 13, 95-115.
10. Bickel, J. P. and D. A. Freedman (1981), 'Some asymptotic theory for the bootstrap'. Annals of Statistics 9, 1196-1217.
11. Bickel, J. P. and A. Sakov (2008), 'On the choice of m in the m out of n bootstrap and confidence bounds for extrema'. Statistica Sinica 18, 967-985.
12. Bogetoft, P. (1996), 'DEA on relaxed convexity assumptions'. Manag-ment Science 42, 457-465. (Pubitemid 126549504)
13. Bogetoft, P., J. M. Tama, and J. Tind (2000), 'Convex input and output projections of nonconvex production possibility sets'. Management Science 46, 858-869.
14. Bretagnolle, J. (1983), 'Lois limites du bootstrap des certaines fonctionnelles'. Annales de l'Institut Henri Poincare (Section B) 19, 223-234.
15. Briec, W., K. Kerstens, and P. Van den Eeckaut (2004), 'Non-convex technologies and cost functions: Definitions, duality, and nonparametric tests of convextiy'. Journal of Economics 81, 155-192. (Pubitemid 38397550)
16. Bǎdin, L., C. Daraio, and L. Simar (2010), 'Optimal bandwidth selection for conditional efficiency measures: A data-driven approach'. European Journal of Operational Research 201, 633-664.
17. Bǎdin, L., C. Daraio, and L. Simar (2012a), 'Explaining inefficiency in nonparametric production models: The state of the art'. Annals of Operations Research, Forthcoming.
18. Bǎdin, L., C. Daraio, and L. Simar (2012b), 'How to measure the impact of environmental factors in a nonparametric production model'. European Journal of Operational Research 223, 818-833.
19. Bǎdin, L. and L. Simar (2009), 'A bias-corrected nonparametric envelopment estimator of frontiers'. Econometric Theory 25, 1289-1318.
20. Cameron, C. A. and P. K. Trivedi (2005), Microeconometrics: Methods and Applications. Cambridge: Cambridge University Press.
21. Cazals, C., J. P. Florens, and L. Simar (2002), 'Nonparametric frontier estimation: A robust approach'. Journal of Econometrics 106, 1-25.
22. Chambers, G. R., Y. Chung, and R. Färe (1996), 'Benefit and distance functions'. Journal of Economic Theory 70, 407-419. (Pubitemid 126159727)
23. Charnes, A., W. W. Cooper, and E. Rhodes (1978), 'Measuring the efficiency of decision making units'. European Journal of Ope rational Research 2, 429-444. (Pubitemid 9402758)
24. Charnes, A., W. W. Cooper, and E. Rhodes (1981), 'Evaluating program and managerial efficiency: An application of data envelopment analysis to program follow through'. Management Science 27, 668-697.
25. Coelli, T., D. S. P. Rao, and G. E. Battese (1997), An Introduction to Efficiency and Productivity Analysis. Boston: Kluwer Academic Publishers.
26. Cook, D. R. and S. Weisberg (1982), Residuals and Influence in Regression. New York: Chapman and Hall.
27. Daouia, A., J. P. Florens, and L. Simar (2008), 'Functional convergence of quantile-type frontiers with application to parametric approximations'. Journal of Statistical Planning and Inference 138, 708-725.
28. Daouia, A., J. P. Florens, and L. Simar (2010), 'Frontier estimation and extreme value theory'. Bernoulli 16, 1039-1063.
29. Daouia, A., J. P. Florens, and L. Simar (2012), 'Regularization of non-parametric frontier estimators'. Journal of Econometrics 168, 285-299.
30. Daouia, A. and I. Gijbels (2011a), 'Estimating frontier cost models using extremiles'. In: I. Van Keilegom and P. W. Wilson (eds.): Exploring Research Frontiers in Contemporary Statistics and Econometrics. Springer-Verlag: Berlin, pp. 65-81.
31. Daouia, A. and I. Gijbels (2011b), 'Robustness and inference in non-parametric partial frontier modeling'. Journal of Econometrics 161, 147-165.
32. Daouia, A. and A. Ruiz-Gazen (2006), 'Robust nonparametric frontier estimators: Qualitative robustness and influence function'. Statistica Sinica 16, 1233-1253.
33. Daouia, A. and L. Simar (2005), 'Robust nonparametric estimators of monotone boundaries'. Journal of Multivariate Analysis 96, 311-331. (Pubitemid 41447902)
34. Daouia, A. and L. Simar (2007), 'Nonparametric efficiency analysis: A multivariate conditional quantile approach'. Journal of Econometrics 140, 375-400. (Pubitemid 47223537)
35. Daraio, C. and L. Simar (2005), 'Introducing environmental variables in nonparametric frontier models: A probabilistic approach'. Journal of Productivity Analysis 24, 93-121. (Pubitemid 41202615)
36. Daraio, C. and L. Simar (2007a), Advanced Robust and Nonparametric Methods in Efficiency Analysis. New York: Springer Science+Business Media, LLC.
37. Daraio, C. and L. Simar (2007b), 'Conditional nonparametric frontier models for convex and nonconvex technologies: A unifying approach'. Journal of Productivity Analysis 28, 13-32.
38. Debreu, G. (1951), 'The coefficient of resource utilization'. Econometrica 19, 273-292.
39. Deprins, D., L. Simar, and H. Tulkens (1984), 'Measuring labor inefficiency in post offices'. In: M. M. P. Pestieau and H. Tulkens (eds.): The Performance of Public Enterprises: Concepts and Measurements. Amsterdam: North-Holland, pp. 243-267.
40. Efron, B. (1979), 'Bootstrap methods: Another look at the jackknife'. Annals of Statistics 7, 1-16.
41. Efron, B. (1982), The Jackknife, the Bootstrap and Other Resampling Plans. Philadelphia: Society for Industrial and Applied Mathematics. CBMS-NSF Regional Conference Series in Applied Mathematics, #38.
42. Efron, B. and R. J. Tibshirani (1993), An Introduction to the Bootstrap. London: Chapman and Hall.
43. Fan, Y., Q. Li, and A. Weersink (1996), 'Semiparametric estimation of stochastic production frontier models'. Journal of Business and Economic Statistics 14, 460-468.
44. Färe, R. (1988), Fundamentals of Production Theory. Berlin: Springer-Verlag.
45. Färe, R., S. Grosskopf, and C. A. K. Lovell (1985), The Measurement of Efficiency of Production. Boston: Kluwer-Nijhoff Publishing.
46. Färe, R., S. Grosskopf, and D. Margaritis (2008), 'Productivity and efficiency: Malmquist and more'. In: H. Fried, C. A. K. Lovell, and S. Schmidt (eds.): The Measurement of Productive Efficiency, chapter 5. Oxford: Oxford University Press, 2nd edition, pp. 522-621.
47. Farrell, J. M. (1957), 'The measurement of productive efficiency'. Journal of the Royal Statistical Society A 120, 253-281.
48. Florens, P. J. and L. Simar (2005), 'Parametric approximations of non-parametric frontiers'. Journal of Economietrics 124, 91-116.
49. Gijbels, I., E. Mammen, B. U. Park, and L. Simar (1999), 'On estimation of monotone and concave frontier functions'. Journal of the American Statistical Association 94, 220-228.
50. Hadley, G. (1962), Linear Programming. Reading, Pennsylvania: Addison-Wesley, Inc.
51. Hall, P. (1992), The Bootstrap and Edgeworth Expansion. New York: Springer-Verlag.
52. Hall, P. and L. Simar (2002), 'Estimating a changepoint, boundary or frontier in the presence of observation error'. Journal of the American Statistical Association 97, 523-534.
53. Hsu, L. P. and H. Robbins (1947), 'Complete convergence and the law of large numbers'. Proceedings of the National Academy of Sciences of the United States of America 33, 25-31.
54. Jeong, O. S., B. U. Park, and L. Simar (2010), 'Nonparametric conditional efficiency measures: asymptotic properties'. Annals of Operational Research 173, 105-122.
55. Jeong, O. S. and L. Simar (2006), 'Linearly interpolated FDH efficiency score for nonconvex frontiers'. Journal of Multivariate Analysis 97, 2141-2161. (Pubitemid 44469202)
56. *'. Pacific Journal of Mathematics 51, 477-481.
57. Johnson, R. C. (1974b), 'Hadamard products of matrices'. Linear and Multilinear Algebra 1, 295-307.
58. Jondrow, J., 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 19, 233-238.
59. Kneip, A., B. Park, and L. Simar (1998), 'A note on the convergence of nonparametric DEA efficiency measures'. E conometric Theory 14, 783-793. (Pubitemid 128656227)
60. Kneip, A., L. Simar, and I. Van Keilegom (2012a), 'Boundary estimation in the presence of measurement error with unknown variance'. Discussion paper #2012/02, Institut de Statistique Biostatistique et Sciences Actuarielles, Université Catholique de Louvain, Louvain-la-Neuve, Belgium.
61. Kneip, A., L. Simar, and P. W. Wilson (2008), 'Asymptotics and consistent bootstraps for DEA estimators in non-parametric frontier models'. Econometric Theory 24, 1663-1697.
62. Kneip, A., L. Simar, and P. W. Wilson (2011), 'A computationally efficient, consistent bootstrap for inference with non-parametric DEA estimators'. Computational Economics 38, 483-515.
63. Kneip, A., L. Simar, and P. W. Wilson (2012b), 'Central limit theorems for DEA scores: When bias can kill the variance'. Discussion paper #2012/xx, Institut de Statistique Biostatistique et Sciences Actuarielles, Université Catholique de Louvain, Louvain-la-Neuve, Belgium.
64. Koenker, R. and G. Bassett (1978), 'Regression quantiles'. Econometrica 46, 33-50.
65. Koopmans, C. T. (1951), 'An analysis of production as an efficient combination of activities'. In: T. C. Koopmans (ed.): Activity Analysis of Production and Allocation. New York: John-Wiley and Sons, Inc., pp. 33-97. Cowles Commission for Research in Economics, Monograph 13.
66. Korostelev, A., L. Simar, and A. B. Tsybakov (1995a), 'Efficient estimation of monotone boundaries'. The Annals of Statistics 23, 476-489.
67. Korostelev, A., L. Simar, and A. B. Tsybakov (1995b), 'On estimation of monotone and convex boundaries'. Publications de l'Institut de Statistique de l'Université de Paris XXXIX 1, 3-18.
68. Kumbhakar, C. S., B. U. Park, L. Simar, and E. G. Tsionas (2007), 'Nonparametric stochastic frontiers: A local likelihood approach'. Journal of Econometrics 137, 1-27. (Pubitemid 46161958)
69. Kuosmanen, T. and M. Kortelainen (2012), 'Stochastic non-smooth envelopment of data: Semi-parametric frontier estimation subject to shape constraints'. Journal of Productivity Analysis 38, 11-28.
70. Marcus, M. and N. Kahn (1959), 'A note on the Hadamard product'. Canadian Mathematical Bulletin 2, 81-93.
71. Marcus, M. and R. C. Thompson (1963), 'The field of values of the Hadamard product'. Archiv der Mathematik 14, 283-288.
72. Meeusen, W. and J. van den Broeck (1977), 'Efficiency estimation from Cobb-Douglas production functions with composed error'. International Economic Review 18, 435-444.
73. Olesen, B. O., N. C. Petersen, and C. A. K. Lovell (1996), 'Summary of the workshop discussion'. Journal of Productivity Analysis 7, 341-345.
74. Park, U. B., S.-O. Jeong, and L. Simar (2010), 'Asymptotic distribution of conical-hull estimators of directional edges'. Annals of Statistics 38, 1320-1340.
75. Park, U. B., L. Simar, and C. Weiner (2000), 'FDH efficiency scores from a stochastic point of view'. Econometric Theory 16, 855-877.
76. Park, U. B., L. Simar, and V. Zelenyuk (2008), 'Local likelihood estimation of truncated regression and its partial derivative: Theory and application'. Journal of Econometrics 146, 185-2008.
77. Politis, N. D. and J. P. Romano (1994), 'Large sample confidence regions based on subsamples under minimal assumtions'. Annals of Statistics 22, 2031-2050.
78. Politis, N. D. and J. P. Romano (1999), Subsampling. New York: Springer-Verlag, Inc.
79. Politis, N. D., J. P. Romano, and M. Wolf (2001), 'On the asymptotic theory of subsampling'. Statistica Sinica 11, 1105-1124. (Pubitemid 33669788)
80. Porembski, M., K. Breitenstein, and P. Alpar (2005), 'Visualizing efficiency and reference relations in data envelopment analysis with an application to the branches of a German bank'. Journal of Productivity Analysis 23, 203-221. (Pubitemid 40630764)
81. Racine, J. and Q. Li (2004), 'Nonparametric estimation of regression functions with both categorical and continuous data'. Journal of Econometrics 119, 99-130.
82. Ritter, C. and L. Simar (1997), 'Pitfalls of normal-gamma stochastic frontier models'. Journal of Productivity Analysis 8, 167-182. (Pubitemid 127429726)
83. Robinson, M. P. (1988), 'Root-n-consistent semiparametric regression'. Econometrica 56, 931-954.
84. Schuster, F. E. (1985), 'Incorporating support constraints into nonparametric estimators of densities'. Communications in Statistics-Theory and Methods 14, 1123-1136.
85. Scott, D. (1992), Multivariate Density Estimation: Theory, Practice, and Visualization. New York: John Wiley & Sons, Inc.
86. Serfling, J. R. (1980), Approximation Theorems of Mathematical Statistics. New York: John Wiley & Sons, Inc.
87. Sheather, J. S. and M. C. Jones (1991), 'A reliable data-based bandwidth selection method for kernel density estimation'. Journal of the Royal Statistical Society, Series B 53, 683-690.
88. Shephard, W. R. (1970), Theory of Cost and Production Functions. Princeton: Princeton University Press.
89. Silverman, W. B. (1978), 'Choosing the window width when estimating a density'. Biometrika 65, 1-11.
90. Silverman, W. B. (1986), Density Estimation for Statistics and Data Analysis. London: Chapman and Hall.
91. Simar, L. (1996), 'Aspects of statistical analysis in DEA-type frontier models'. Journal of Productivity Analysis 7, 177-185. (Pubitemid 126716677)
92. Simar, L. (2003), 'Detecting outliers in frontier models: A simple approach'. Journal of Productivity Analysis 20, 391-424. (Pubitemid 39045900)
93. Simar, L. (2007), 'How to improve the performances of DEA/FDH estimators in the presence of noise'. Journal of Productivity Analysis 28, 183-201.
94. Simar, L. and A. Vanhems (2012), 'Probabilistic characterization of directional distances and their robust versions'. Journal of Econometrics 166, 342-354.
95. Simar, L., A. Vanhems, and P. W. Wilson (2012), 'Statistical inference for dea estimators of directional distances'. European Journal of Operational Research 220, 853-864.
96. Simar, L. and P. W. Wilson (1998), 'Sensitivity analysis of efficiency scores: How to bootstrap in nonparametric frontier models'. Management Science 44, 49-61. (Pubitemid 128569642)
97. Simar, L. and P. W. Wilson (1999a), 'Estimating and bootstrapping Malmquist indices'. European Journal of Operational Research 115, 459-471.
98. Simar, L. and P. W. Wilson (1999b), 'Of course we can bootstrap DEA scores! but does it mean anything? logic trumps wishful thinking'. Journal of Productivity Analysis 11, 93-97.
99. Simar, L. and P. W. Wilson (1999c), 'Some problems with the Ferrier/Hirschberg bootstrap idea'. Journal of Productivity Analysis 11, 67-80.
100. Simar, L. and P. W. Wilson (2000a), 'A general methodology for bootstrapping in non-parametric frontier models'. Journal of Applied Statistics 27, 779-802.
101. Simar, L. and P. W. Wilson (2000b), 'Statistical inference in nonparametric frontier models: The state of the art'. Journal of Productivity Analysis 13, 49-78.
102. Simar, L. and P. W. Wilson (2001a), 'Nonparametric tests of returns to scale'. European Journal of Operational Research 139, 115-132.
103. Simar, L. and P. W. Wilson (2001b), 'Testing restrictions in nonparametric efficiency models'. Communications in Statistics 30, 159-184. (Pubitemid 33790993)
104. Simar, L. and P. W. Wilson (2007), 'Estimation and inference in two-stage, semi-parametric models of productive efficiency'. Journal of Econometrics 136, 31-64. (Pubitemid 44380324)
105. Simar, L. and P. W. Wilson (2008), 'Statistical inference in nonparametric frontier models: Recent developments and perspectives'. In: H. Fried, C. A. K. Lovell, and S. Schmidt (eds.): The Measurement of Productive Efficiency, chapter 4. Oxford: Oxford University Press, 2nd edition, pp. 421-521.
106. Simar, L. and P. W. Wilson (2010), 'Estimation and inference in cross-sectional, stochastic frontier models'. Econometric Reviews 29, 62-98.
107. Simar, L. and P. W. Wilson (2011a), 'Inference by the m out of n bootstrap in nonparametric frontier models'. Journal of Productivity Analysis 36, 33-53.
108. Simar, L. and P. W. Wilson (2011b), 'Two-Stage DEA: Caveat emptor'. Journal of Productivity Analysis 36, 205-218.
109. Simar, L. and V. Zelenyuk (2011), 'Stochastic FDH/DEA estimators for frontier analysis'. Journal of Productivity Analysis 36, 1-20.
110. Swanepoel, J. W. H. (1986), 'A note on proving that the (modified) bootstrap works'. Communications in Statistics: Theory and Methods 15, 3193-3203.
111. Wheelock, C. D. and P. W. Wilson (2003), 'Robust nonparametric estimation of efficiency and technical change in U. S. commercial banking'. Unpublished working paper, The John E. Walker Department of Economics, 222 Sirrine Hall, Clemson University, Clemson, South Carolina 29634, USA.
112. Wheelock, C. D. and P. W. Wilson (2008), 'Non-parametric, unconditional quantile estimation for efficiency analysis with an application to Federal Reserve check processing operations'. Journal of Econometrics 145, 209-225.
113. Wheelock, C. D. and P. W. Wilson (2011), 'Are credit unions too small?'. Review of Economics and Statistics 93, 1343-1359.
114. Wilson, W. P. (1993), 'Detecting outliers in deterministic nonparametric frontier models with multiple outputs'. Journal of Business and Economic Statistics 11, 319-323.
115. Wilson, W. P. (1995), 'Detecting influential observations in data envelopment analysis'. Journal of Productivity Analysis 6, 27-45.
116. Wilson, W. P. (2004), 'A preliminary non-parametric analysis of public education and health expenditures developing countries'. Unpublished working paper, The John E. Walker Department of Economics, 222 Sirrine Hall, Clemson University, Clemson, South Carolina 29634, USA.
117. Wilson, W. P. (2008), 'FEAR: A software package for frontier efficiency analysis with R'. Socio-Economic Planning Sciences 42, 247-254.
118. Wilson, W. P. (2011), 'Asymptotic properties of some non-parametric hyperbolic efficiency estimators'. In: I. Van Keilegom and P. W. Wilson (eds.): Exploring Research Frontiers in Contemporary Statistics and Econometrics. Berlin: Springer-Verlag, pp. 115-150.
119. Wood, S. F. (1973), 'The use of individual effects and residuals in fitting equaitons to data'. Technometrics 15, 677-694.