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Bootstrapping Quantile Regression Estimators

Published online by Cambridge University Press:  11 February 2009

Jinyong Hahn
Jinyong Hahn
Affiliation:
University of Pennsylvania
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Abstract

The asymptotic variance matrix of the quantile regression estimator depends on the density of the error. For both deterministic and random regressors, the bootstrap distribution is shown to converge weakly to the limit distribution of the quantile regression estimator in probability. Thus, the confidence intervals constructed by the bootstrap percentile method have asymptotically correct coverage probabilities.

Type
Articles
Information
Econometric Theory , Volume 11 , Issue 1 , February 1995 , pp. 105 - 121
Copyright
Copyright © Cambridge University Press 1995

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References

REFERENCES

Arcones, M. & Giné, E. (1992) On the bootstrap of M-estimators and other statistical functionals. In LePage, R. & Billard, L. (eds.), Exploring the Limits of Bootstrap, pp. 13–47. New York: Wiley.Google Scholar
Babu, G.J. (1986) A note on bootstrapping the variance of sample quantile. Annals of the Institute of Statistical Mathematics 38 (A), 439–443.CrossRefGoogle Scholar
Bickel, P.J. & Freedman, D.A. (1981) Some asymptotic theory for the bootstrap. Annals of Statistics 9, 1196–1217.CrossRefGoogle Scholar
Billingsley, P. (1979) Probability and Measure. New York: Wiley.Google Scholar
Bloomfield, P. & Steiger, W.L. (1983) Least Absolute Deviations: Theory, Applications, and Algorithms. Boston: Birkhauser.Google Scholar
Buchinsky, M. (1991) A Monte Carlo study of the asymptotic covariance matrix estimators for quantile estimators. In The Theory and Practice of Quantile Regression. Ph.D. Dissertation, Harvard University.Google Scholar
Buchinsky, M. (1994) Changes in the U.S. wage structure 1963–1987: Application of quantile regression. Econometrica 62, 405–458.CrossRefGoogle Scholar
Chamberlain, G. (1991) Quantile Regression, Censoring, and the Structure of Wages. Discussion paper 1558, Harvard Institute of Economic Research.Google Scholar
Chung, K.L. (1974) A Course in Probability Theory. San Diego: Academic Press.Google Scholar
Efron, B. (1982) The Jackknife, the Bootstrap and Other Resampling Plans. CBMS-NSF Regional Conference Series in Applied Mathematics 38.CrossRefGoogle Scholar
Ghosh, M., Parr, W.C.Singh, K. & Babu, G.J. (1984) A note on bootstrapping the sample median. Annals of Statistics 12, 1130–1135.CrossRefGoogle Scholar
Giné, E. & Zinn, J. (1990) Bootstrapping general empirical measures. Annals of Probability 18, 851–869.CrossRefGoogle Scholar
Koenker, R. & Bassett, G.S. Jr., (1978) Regression quantiles. Econometrica 46, 33–50.CrossRefGoogle Scholar
Koenker, R. & Bassett, G.S. Jr., (1982) Robust tests for heteroscedasticity based on regression quantiles. Econometrica 50, 43–61.CrossRefGoogle Scholar
Oberhofer, W. (1982) The consistency of nonlinear regression minimizing the L 1 norm. Annals of Statistics 10, 316–319.CrossRefGoogle Scholar
Pakes, A. & Pollard, D. (1989) Simulation and the asymptotics of optimization estimators. Econometrica 57, 1027–1057.CrossRefGoogle Scholar
Pollard, D. (1985) New ways to prove central limit theorems. Econometric Theory 1, 295–314.CrossRefGoogle Scholar
Pollard, D. (1990) Empirical processes: Theory and applications. In Regional Conference Series in Probability and Statistics, vol. 2. Institute of Mathematical Statistics.Google Scholar
Pollard, D. (1991) Asymptotics for least absolute deviation regression estimators. Econometric Theory 7, 186–199.CrossRefGoogle Scholar
Powell, J. (1984) Least absolute deviations estimation for the censored regression model. Journal of Econometrics 25, 303–325.CrossRefGoogle Scholar
Powell, J. (1986) Censored regression quantiles. Journal of Econometrics 32, 143–155.CrossRefGoogle Scholar
Powell, J. (1991) Estimation of raonotonic regression models under quantile restrictions. In Barnett, W., Powell, J., & Tauchen, G. (eds.), Nonparametric and Semiparametric Methods in Econometrics and Statistics. Cambridge: Cambridge University Press.Google Scholar