Local asymptotics for quantile smoothing splines

Annals of Statistics

Volumn 25, Issue 1, 1997, Pages 414-434

  Portnoy, Stephen ^a  

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

Author keywords

Conditional quantiles; Nonparametric regression; Rates of convergence

Indexed keywords

EID: 0031530602     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1034276636     Document Type: Article

References (17)

1. GUTENBRUNNER, C., JUREČKOVÁ, J., KOENKER, R. and PORTNOY, S. (1993). Tests of linear hypotheses based on regression rank scores. J. Nonparametric Statist. 2 307-331.
2. HE, X. and SHI, P. (1994). Convergence rate of B-spline estimators of nonparametric conditional quantile functions. J. Nonparametric Statist. 3 299-308.
3. HENDRICKS, W. and KOENKER, R. (1992). Hierarchical spline models for conditional quantiles and the demand for electricity. J. Amer. Statist. Assoc. 87 58-68.
4. HURVICH, C. and TSAI, C.-L. (1989). Model selection in small samples. Biometrika 76 297-307.
5. JUREČKOVÁ, J. (1977). Asymptotic relations of M-estimates and R-estimates in linear regression model. Ann. Statist. 5 464-472.
6. KOENKER, R. and BASSETT G. (1978). Regression quantiles. Econometrica 46 33-50.
7. KOENKER, R., NG, P. T. and PORTNOY, S. (1994). Quantile smoothing splines. Biometrika 81 673-680.
8. KOOPERBERG, C. and STONE, C. (1991). A study of logspline density estimation. Comput. Statist. Data Anal. 12 327-347.
9. MAMMEN, E. (1991). Nonparametric regression under qualitative smoothness assumptions. Ann. Statist. 19 741-759.
10. MAMMEN, E. and VAN DE GEER, S. (1997). Locally adaptive regression splines. Ann. Statist. 25 387-413.
11. PORTNOY, S. (1991). Asymptotic behavior of regression quantiles in non-stationary dependent cases. J. Multivariate Anal. 38 100-113.
12. PORTNOY, S. and KOENKER, R. (1989). Adaptive L-estimation for linear models. Ann. Statist. 17 362-381.
13. SCHWARZ, G. (1978). Estimating the dimension of a model. Ann. Statist, 6 461-464.
14. SHEN, X. (1994). On the method of penalization. Technical report, Dept. Statistics, Ohio State Univ.
15. SHORACK, G. and WELLNER, J. (1986). Empirical Processes with Applications to Statistics. Wiley, New York.
16. WANG, Y. (1993). The limiting distribution in concave regression. Technical report, Univ. Missouri-Columbia.
17. WELSH, A. (1989). On M-processes and M-estimation. Ann. Statist. 17 337-361.