# Inference on the Quantile Regression Process

## Author Info

Listed author(s):
• Roger Koenker

(University of Illinois)

Registered author(s):

## Abstract

Quantile regression is gradually evolving into a comprehensive approach to the statistical analysis of linear and nonlinear response models for conditional quantile functions. Just as classical linear regression methods based on minimizing sums of squared residuals enable one to estimate models for conditional mean functions, quantile regression methods based on minimizing asymmetrically weighted {\it absolute} residuals offer a mechanism for estimating models for the conditional median function, and the full Tests based on the quantile regression process can be formulated like the classical Kolmogorov-Smirnov and Cramer-von-Mises tests of goodness-of-fit employing the theory of Bessel processes as in Kiefer (1959). However, it is frequently desirable to formulate hypotheses involving unknown nuisance parameters, thereby jeopardizing the distribution free character of these tests. We characterize this situation as the Durbin problem'' since it was posed in Durbin (1973), for parametric empirical processes. In this paper we consider an approach to the Durbin problem involving a martingale transformation of the parametric empirical process suggested by Khmaladze (1981) and show that it can be adapted to a wide variety of inference problems involving the quantile regression process. In particular, we suggest new tests of the location shift and location-scale shift models that underlie much of classical econometric inference. The methods are illustrated in some limited Monte-Carlo experiments and with a reanalysis of data on unemployment durations from the Pennsylvania Reemployment Bonus Experiments. The Pennsylvania experiments, conducted in 1988-89, were designed to test the efficacy of cash bonuses paid for early reemployment in shortening the duration of insured unemployment spells.

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File URL: http://fmwww.bc.edu/RePEc/es2000/0886.pdf
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## Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 0886.

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 Length: Date of creation: 01 Aug 2000 Handle: RePEc:ecm:wc2000:0886 Contact details of provider: Phone: 1 212 998 3820Fax: 1 212 995 4487Web page: http://www.econometricsociety.org/pastmeetings.aspEmail: More information through EDIRC

## References

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1. Joel L. Horowitz, 1998. "Bootstrap Methods for Median Regression Models," Econometrica, Econometric Society, vol. 66(6), pages 1327-1352, November.
2. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
3. Hahn, Jinyong, 1995. "Bootstrapping Quantile Regression Estimators," Econometric Theory, Cambridge University Press, vol. 11(01), pages 105-121, February.
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