Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-23T21:53:35.729Z Has data issue: false hasContentIssue false
  • English
  • Français

ASYMPTOTIC PROPERTIES OF NONPARAMETRIC FRONTIER ESTIMATORS

Published online by Cambridge University Press:  09 July 2008

Lajos Horváth ,
Zsuzsanna Horváth  and
Wang Zhou
Lajos Horváth*
Affiliation:
University of Utah
Zsuzsanna Horváth
Affiliation:
University of Utah
Wang Zhou
Affiliation:
National University of Singapore
*
Address correspondence to Lajos Horváth, Department of Mathematics, University of Utah, 155 South 1440 East, Salt Lake City, UT 84112-0090, USA; e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Aragon, Daouia, and Thomas-Agnan (2005, Econometric Theory 21, 358–389) introduced a new nonparametric frontier estimation. We prove the weak convergence of the empirical conditional quantile function. The distribution of the limit depends on the unknown conditional quantile density function. We provide a method to construct uniform confidence bands without estimating the conditional quantile density.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 6 , December 2008 , pp. 1607 - 1627
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Aragon, Y., Daouia, A., & Thomas-Agnan, C. (2005) Nonparametric frontier estimation: A conditional quantile-based approach. Econometric Theory 21, 358–389.CrossRefGoogle Scholar
Bickel, P.J. & Freedman, D.A. (1981) Some asymptotic theory for the bootstrap. Annals of Statistics 9, 1196–1217.CrossRefGoogle Scholar
Cazals, C., Florens, J.P., & Simar, L. (2002) Nonparametric frontier estimation: A robust approach. Journal of Econometrics 1, 1–25.CrossRefGoogle Scholar
Chung, C.-J., Csörgő, M., & Horváth, L. (1990) Confidence bands for quantile function under random censorship. Annals of the Institute of Statistical Mathematics 42, 21–36.CrossRefGoogle Scholar
Csörgő, M. & Horváth, L. (1989) On confidence bands for the quantile function of a continuous distribution function. In Berkes, I., Czáki, E., & Révész, P. (eds.), Colloquia Mathematica Societatis János Bolyai, vol. 57, Limit Theorems of Probability Theory and Statistics, pp. 95–106. North-Holland.Google Scholar
Csörgő, M. & Horváth, L. (1993) Weighted Approximations in Probability and Statistics. Wiley.Google Scholar
Csörgő, M. & Révész, P. (1984) Two approaches to constructing simultaneous confidence bounds for quantiles. Probability and Mathematical Statistics 4, 221–236.Google Scholar
Daouia, A. (2005) Asymptotic representation theory for nonstandard conditional quantiles. Nonparametric Statistics 17, 253–268.CrossRefGoogle Scholar
Debreu, G. (1951) The coefficient of resource utilization. Econometrica 19, 273–292.CrossRefGoogle Scholar
Horváth, L. (1984) Strong approximation of renewal processes. Stochastic Processes and Their Applications 18, 127–138.CrossRefGoogle Scholar
Koopmans, T.C. (1951) An analysis of production as an efficient combination of activities. In Koopmans, T.C. (ed.), Activity Analysis of Production and Allocation, Cowles Commission for Research in Economics, Monograph 13. Wiley.Google Scholar
Philipp, W. & Pinzur, L. (1980) Almost sure approximation theorems for the multivariate empirical process. Zeitschrift für Wahrscheinlichskeitstheorie und Verwandte Gebiete 54, 1–13.CrossRefGoogle Scholar
Shephard, R.W. (1970) Theory of Costs and Production Function. Princeton University Press.Google Scholar
Shorack, G.R. & Wellner, J.A. (1986) Empirical Processes with Applications to Statistics. Wiley.Google Scholar
Silverman, B.W. (1986) Density Estimation for Statistics and Data Analysis. Chapman and Hall.Google Scholar
Tsirelson, B.S. (1975) Density of the distribution of the maximum of a Gaussian process (in Russian). Teorija Verojatnosty i Primenen 20, 865–873.Google Scholar
Wichura, M.J. (1973) Some Strassen-type laws of the iterated logarithm for multiparameter stochastic processes with independent increments. Annals of Probability 1, 272–296.CrossRefGoogle Scholar