Statistical inference on heteroscedastic models based on regression quantiles

Journal of Nonparametric Statistics

Volumn 9, Issue 3, 1998, Pages 239-260

  Zhou, Kenneth Q ^a   Portnoy, Stephen L ^a  

^a UNIVERSITY OF ROCHESTER   (United States)

Author keywords

Bahadur representation; Brownian bridge; Conditional quantiles; Direct method; Empirical levels; LAD residuals

Indexed keywords

EID: 0345124540     PISSN: 10485252     EISSN: None     Source Type: Journal    
DOI: 10.1080/10485259808832745     Document Type: Article

References (26)

1. Amemiya, T. (1973) Regression analysis when the variance of the dependent variable is proportional to the square of its expectation, J. Ameri. Statist. Assoc., 68, 928-934.
2. Bai, Z. D., Chen, X. R., Miao, B. Q. and Rao, C. R. (1990) Asymptotic Theory of Least Distances Estimate in Multivariate Models, Statistics, 21, 503-519.
3. Bassett, G. W. and Koenker, R. W. (1982a) Robust tests for heteroscedasticity based on regression quantiles, Econometrica, 50, 43-61.
4. Bassett, G. W. and Koenker, R. W. (1982b) An empirical quantile function for linear models with i.i.d. errors, J. Ameri. Statist. Assoc., 77, 407-415.
5. Bassett, G. W. and Koenker, R. W. (1986) Strong consistency of regression quantiles and related empirical processes, Econometric Theory, 2, 191-201.
6. Bofinger, E. (1975) Estimation of a density function using order statistics, Australian J. of Statist., 17, 1-7.
7. Carroll, R. J. and Ruppert, D. (1980) Transformation and Weighting in Regression, Chapman and Hall, London, 1988.
8. Goldfeld, S. M. and Quandt, R. E. (1965) Some tests for heteroscedasticity, J. Ameri. Statist. Assoc., 60, 539-547.
9. Gutennbrunner, C. and Jurečková, J. (1992) Regression rank-scores and regression quantiles, Ann. Statist., 20, 305-330.
10. Gutennbrunner, C., Jurečková, J., Koenker, R. W. and Portnoy, S. (1992) Tests of linear hypotheses based on regression rank scores, J. Nonparametric statistics, 2, 307-331.
11. Hall, P. and Sheather, S. J. (1988) On the distribution of a studentized quantile, J. Roy. Statist. Soc. Ser. B., 50, 381-391.
12. Harvey, A. C. (1976) Estimating regression models with multiplicative heteroscedasticity, Econometrica, 44, 461-466.
13. He, X. and Shao, Q. (1996) A general Bahadur's representation for M-estimators and its application to linear regression with nonstochastic designs, Ann. Statist., 24, 2608-2630.
14. Jurečková, J. (1977) Asymptotic relations of M-estimates and R-estimates in linear regression model, Ann. Statist., 5, 464-472.
15. Koenker, R. W. and Bassett, G. W. (1978) Regression quantiles, Econometrica, 46, 33-50.
16. Koenker, R. W. and Portnoy, S. (1987) L-estimation in linear model, J. Ameri. Statist. Assoc., 82, 851-857.
17. Koenker, R. W. and Zhao, Q. (1994) L-estimation for heterodastic linear models, J. Nonparametric Stat., 3, 223-235.
18. Koenker, R. W. and D'Orey (1987) Computing regression quantiles, Appl. Statist., 36, 383-393.
19. Meyer, J. R. and Kuh, E. (1957) The analysis of family budgets, Cambridge University Press, Cambridge.
20. Portnoy, S. and Koenker, R. W. (1989) Adaptive L-estimates of linear models, Ann. Statist., 17, 362-381.
21. Ruppert, D. and Carroll, R. J. (1980) Trimmed least squared estimation in the linear model, J. Ameri. Statist. Assoc., 75, 828-838.
22. Serfling, R. (1980) Approximation theory of mathematical statistics, New York, John Wiley.
23. Ying, Z., Jung, S. H. and Wei, L. J. (1995) Survival analysis with median regression models, J. Ameri. Statist. Assoc., 90, 178-184.
24. Weisberg, S. (1985) Applied linear regression. New York, John Wiley.
25. Zhou, K. Q. and Portnoy, L. S. (1994) Direct use of regression quantiles to construct confidence sets in linear models, Ann. of Statist., 24, 287-306.
26. Zhou, K. Q. (1995) Quantile regression and survival analysis, Ph. D. Dissertation, University of Illinois at Urbana-Champaign.