Abstract
This paper demonstrates that the bootstrap procedure suggested by Ferrier and Hirschberg (1997) gives inconsistent estimates. A very simple example is given to illustrate the statistical issues underlying nonparametric efficiency measurement and the problems with the Ferrier/Hirschberg approach, and may serve as a primer on bootstrapping in nonparametric models of production processes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Atkinson, S. E., and P. W. Wilson. (1992). “The Bias of Bootstrapped Versus Conventional Standard Errors in the General Linear and SUR Models.” Econometric Theory 8, 259–275.
Beran, R., and G. Ducharme. (1991). Asymptotic Theory for Bootstrap Methods in Statistics. Montreal: Centre de Reserches Mathematiques, University of Montreal.
Bickel, P. J., and D. A. Freedman. (1981). “Some Asymptotic Theory for the Bootstrap.” Annals of Statistics 9, 1196–1217.
Bretagnolle, J. (1983). “Lois Limites du Bootstrap de Certaines Fonctionnelles.” Annales de l'Institut Henri Poincare (Section B) 19, 223–234.
Efron, B. (1979). “Bootstrap Methods: Another Look at the Jackknife.” Annals of Statistics 7, 1–16.
Efron, B., and R. J. Tibshirani. (1993). An Introduction to the Bootstrap. New York: Chapman and Hall.
Färe, R. (1988). Fundamentals of Production Theory. Berlin: Springer-Verlag.
Ferrier, G. D., and J. G. Hirschberg. (1997). “Bootstrapping Confidence Intervals for Linear Programming Efficiency Scores: With an Illustration Using Italian Bank Data.” Journal of Productivity Analysis 8, 19–33.
Gijbels, I., E. Mammen, B. U. Park, and L. Simar. (1996). “On Estimation of Monotone and Concave Frontier Functions.” Discussion Paper #9611, Institut de Statistique, Université Catholique de Louvain, Louvain-la-Neuve, Belgium, forthcoming in the Journal of the American Statistical Association.
Grosskopf, S. (1996). “Statistical Inference and Nonparametric Efficiency: A Selective Survey.” Journal of Productivity Analysis 7, 161–176.
Härdle, W. (1990). Applied Nonparametric Regression. Cambridge: Cambridge University Press.
Härdle, W., and E. Mammen. (1993). “Comparing Nonparametric Versus Parametric Regression Fits.” Annals of Statistics 21, 1926–1947.
Härdle, W., and J. S. Marron. (1991). “Bootstrap Simultaneous Error Bars for Nonparametric Regression.” Annals of Statistics 19, 778–796.
Johnson, N. L., S. Kotz, and A. W. Kemp. (1992). Univariate Discrete Distributions (2nd edition). New York: John Wiley & Sons, Inc.
Kneip, A., B. U. Park, and L. Simar. (1998). “A Note on the Convergence of Nonparametric DEA Efficiency Measures.” Econometric Theory 14, 783–793.
Korostelev, A. P., L. Simar, and A. B. Tsybakov. (1995a). “On Estimation of Monotone and Convex Boundaries.” Publications de l'Institut de Statistique de l'Université de Paris 39, 3–18.
Korostelev, A. P., L. Simar, and A. B. Tsybakov. (1995b). “Efficient Estimation of Monotone Boundaries.” Annals of Statistics 23, 476–489.
Simar, L. (1996). “Aspects of Statistical Analysis in DEA-Type Frontier Models.” Journal of Productivity Analysis 7, 177–185.
Simar, L., and P. W. Wilson. (1998a). “Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models.” Management Science 44, 49–61.
Simar, L., and P. W. Wilson (1998b). “Estimating and Bootstrapping Malmquist Indices.” European Journal of Operational Research, forthcoming.
Simar, L., and P. W. Wilson. (1998c). “Nonparametric Tests of Returns to Scale.” Unpublished working paper, Department of Economics, University of Texas, Austin, Texas, USA.
Simar, L., and P. W. Wilson (1998d). “A General Methodology for Bootstrapping in Nonparametric Frontier Models.” Unpublished working paper, L'Institut de Statistique, Université Catholique de Louvain, Louvain-la-Neuve, Belgium.
Shephard, R. W. (1970). Theory of Cost and Production Functions. Princeton University Press, Princeton.
Swanepoel, J. W. H. (1986). “A Note on Proving that the (Modified) Bootstrap Works.” Communications in Statistics: Theory and Methods 15, 3193–3203.
Zelterman, D. (1993). “A Semiparametric Bootstrap Technique for Simulating Extreme Order Statistics.” Journal of the American Statistical Association 88, 477–485.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Simar, L., Wilson, P.W. Some Problems with the Ferrier/Hirschberg Bootstrap Idea. Journal of Productivity Analysis 11, 67–80 (1999). https://doi.org/10.1023/A:1007735422028
Issue Date:
DOI: https://doi.org/10.1023/A:1007735422028