A Lack-of-Fit Test for Quantile Regression

Journal of the American Statistical Association

Volumn 98, Issue 464, 2003, Pages 1013-1022

  He, Xuming ^a   Zhu, Li Xing ^b,c  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

^c INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

Consistency; Cusum process; Empirical process; Goodness of fit; Linear regression; Local alternative; Resampling

Indexed keywords

EID: 1142301687     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214503000000963     Document Type: Article

References (48)

1. Azzalini, A., Bowman, A. W., and Härdle, W. (1989), "On the Use of Nonparametric Regression for Model Checking," Biometrika, 76, 1-11.
2. Bierens, H. J., and Ploberger, W. (1997), "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, 65, 1129-1151.
3. Buckley, M. J. (1991), "Detecting a Smooth Signal: Optimality of Cusum Based Procedures," Biometrika, 78, 253-262.
4. Cox, D. D., Koh, E., Wahba, G., and Yandell, B. S. (1988), "Testing the (Parametric) Null Hypothesis in (Semiparametric) Partial and Generalized Spline Models," The Annals of Statistics, 16, 113-119.
5. Eubank, R. L., and Hart, J. D. (1993), "Commonality of Cusum, von Neumann and Smoothing-Based Goodness-of-Fit Test," Biometrika, 80, 89-98.
6. Eubank, R. L., and Spiegelman, C. H. (1990), "Testing the Goodness of Fit of a Linear Model via Nonparametric Regression Techniques," Journal of the American Statistical Association, 85, 387-392.
7. Fan, J. (1996), "Test of Significance Based on Wavelet Thresholding and Neyman's Truncation," Journal of the American Statistical Association, 91, 674-688.
8. Fan, J., and Huang, L. (2001), "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, 96, 640-652.
9. Fan, J., Zhang, C. M., and Zhang, J. (2001), "Generalized Likelihood Ratio Statistics and Wilks Phenomenon," The Annals of Statistics, 29, 153-193.
10. Gine, E., and Zinn, J. (1984), "On the Central Limit Theorem for Empirical Processes" (with discussion), Annals of Probability, 12, 929-998.
11. Gonzalea-Manteiga, W., and Cao, R. (1993), "Testing the Hypothesis of a General Linear Model Using Nonparametric Regression Estimation," Test, 2, 161-188.
12. Härdle, W., and Mammen, E. (1993), "Comparing Nonparametric Versus Parametric Regression Fits," The Annals of Statistics, 21, 1926-1947.
13. Hart, J. D. (1997), Nonparametric Smoothing and Lack-of-Fit Tests, New York: Springer-Verlag.
14. He, X., and Ng, P. (1999), "Quantile Splines with Several Covariates," Journal of Statistical and Planning Inference, 15, 343-352.
15. He, X., Ng, P., and Portnoy, S. (1998), "Bivariate Quantile Smoothing Splines," Journal of the Royal Statistical Society, Ser. B, 60, 537-550.
16. He, X., and Shao, Q. M. (1996), "A General Bahadur Representation of M -Estimators and Its Application to Linear Regression With Nonstochastic Designs," The Annals of Statistics, 24, 2608-2630.
17. He, X., and Shi, P. D. (1994), "Convergence Rate of B-Spline Estimators of Nonparametric Conditional Quantile Functions," Journal of Nonparametric Statistics, 3, 299-308.
18. Hodges, J. L., Jr. (1957), "The Significance Probability of the Smirnov Two-Sample Test," Arkiv für Matemaiik, 3, 469-486.
19. Hong, Y., and White, H. (1995), "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, 63, 1133-1159.
20. Horowitz, J. L., and Spokoiny, V. G. (2002), "An Adaptive, Rate-Optimal Test of Linearity for Median Regression Models," Journal of the American Statistical Association, 97, 822-835.
21. Ingster, Y. (1993), "Asymptotic Minimax Hypothesis Testing for Nonparametric Alternatives I-III," Mathematical Mehods in Statistics, 2, 85-114; 3, 171-189; 4, 249-268.
22. Ingster, Y. (1993), "Asymptotic Minimax Hypothesis Testing for Nonparametric Alternatives I-III," Mathematical Mehods in Statistics, 2, 85-114; 3, 171-189; 4, 249-268.
23. Ingster, Y. (1993), "Asymptotic Minimax Hypothesis Testing for Nonparametric Alternatives I-III," Mathematical Mehods in Statistics, 2, 85-114; 3, 171-189; 4, 249-268.
24. Jurečková, J., and Procházka, B. (1994), "Regression Quantiles and Trimmed Least Squares Estimator in Nonlinear Regression Model," Journal of Nonparametric Statistics, 3, 201-222.
25. Khmaladze, E. V. (1981), "Martingale Approach in the Theory of Goodness-of-Fit Tests," Theory of Probability and Its Applications, 26, 240-257.
26. Koenker R., and Bassett, G., Jr. (1978), "Regression Quantiles," Econometrica, 46, 33-50.
27. Koenker, R., and d'Orey, V. (1987), "Computing Regression Quantiles," Applied Statistics, 36, 383-393.
28. Koenker, R., Ng, P., and Portnoy, S. (1994), "Quantile Smoothing Spline," Biometrika, 81, 673-680.
29. Koenker, R., and Park, B. J. (1996), "An Interior Point Algorithm for Nonlinear Quantile Regression," Journal of Econometrics, 71, 265-283.
30. Koenker, R., and Zhao, Q. (1994), "L-Estimation for Linear Heteroscedastic Models," Journal of Nonparametric Statistics, 3, 223-235.
31. LaRiccia, V. N. (1991), "Smooth Goodness-of-Fit Tests: A Quantile Function Approach," Journal of the American Statistical Association 86, 427-431.
32. Lepski, O. V., and Spokoiny, V. G. (1999), "Minimax Nonparametric Hypothesis Testing: The Case of an Inhomogeneous Alternative," Bernoulli, 5, 333-358.
33. 1-Norm," The Annals of Statistics, 10, 316-319.
34. Pollard, D. (1984), Convergence of Stochastic Processes, New York: Springer-Verlag.
35. Portnoy, S. L. (1997), "Local Asymptotics for Quantile Smoothing Splines," The Annals of Statistics, 25, 414-434.
36. Shorack, G. R., and Wellner, J. A. (1996), Empirical Processes With Applications to Statistics, New York: Wiley.
37. Spokoiny, V. G. (1996), "Adaptive Hypothesis Testing Using Wavelets," The Annals of Statistics, 24, 2477-2498.
38. Staniswalis, J. G., and Severini, T. A. (1991), "Diagnostics for Assessing Regression Models," Journal of the American Statistical Association, 86, 684-692.
39. Stute, W. (1997), "Nonparametric Model Checks for Regression," The Annals of Statistics, 25, 613-641.
40. Stute, W., Manteiga, G., and Quindimil, M. P. (1998), "Bootstrap Approximations in Model Checks for Regression," Journal of the American Statistical Association, 93, 141-149.
41. Stute, W., Thies, S., and Zhu, L. X. (1998), "Model Checks for Regression: An Innovation Process Approach," The Annals of Statistics, 26, 1916-1934.
42. Stute, W., and Zhu, L. X. (2002), "Model Checks for Generalized Linear Models," Scandinavian Journal of Statistics 29, 535-546.
43. Wooldridge, J. (1992), "A Test for Functional Form Against Nonparametric Alternatives," Econometric Theory, 8, 452-475.
44. Yatchew, A. J. (1992), "Nonparametric Regression Tests Based on an Infinite Dimensional Least Squares Procedure," Econometric Theory, 8, 435-451.
45. Zhao, Q. (2001), "Asymptotically Efficient Median Regression in the Presence of Heteroscedasticity of Unknown Form," Econometric Theory, 17, 765-784.
46. Zheng, J. X. (1998), "A Consistent Nonparametric Test of Parametric Regression Models Under Conditional Quantile Restrictions," Econometric Theory, 14, 123-138.
47. Zhu, L. X. (1993), "Convergence Rates of Empirical Processes Indexed by the Class of Functions With Applications," Journal of Systems Science and Mathematical Sciences, 13, 33-41 (in Chinese).
48. _ (2003), "Model Checking of Dimension-Reduction Type for Regression," Statistica Sinica, 13, 283-296.