On spline estimators and prediction intervals in nonparametric regression

Computational Statistics and Data Analysis

Volumn 35, Issue 1, 2000, Pages 67-82

  Doksum, Kjell ^a   Koo, Ja Yong ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b Hallym University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL GEOMETRY; LINEAR PROGRAMMING; MATHEMATICAL MODELS; PARAMETER ESTIMATION; POLYNOMIALS;

HETEROSCEDASTIC LINEAR MODELS; QUANTILE REGRESSION FUNCTIONS;

REGRESSION ANALYSIS;

EID: 0034315586     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-9473(99)00116-4     Document Type: Article

References (28)

1. H Akaike A new look at the statistical model identification IEEE Trans. Automat. Control. 19 1974 716 723
2. 1 linear approximation SIAM J. Numer. Anal. 10 1973 839 848
3. 1 norm Comm. ACM 17 1973 319 320
4. G Bassett R Koenker The asymptotic distribution of the least absolute error distribution J. Amer. Statist. Assoc. 73 1978 618 622
5. C de Boor A Practical Guide to Splines 1978 Springer New York
6. L Breiman J Friedman Estimating optimal transformations for multiple regression and correlation J. Amer. Statist. Assoc. 80 1985 580 598
7. L Breiman S Peters Comparing automatic smoothers (A public service enterprise) Int. Statist. Rev. 60 1992 271 290
8. P Chaudhuri Nonparametric estimates of regression quantiles and their local Bahadur representation Ann. Statist. 19 1991 760 777
9. R Chappel Fitting bend lines to data, with applications to allometry. D. Theor. Biol. 138 1989 235 256
10. P Chaudhuri K Doksum A Samarov On average derivative quantile regression Ann. Statist. 25 1997 715 744
11. K Doksum A Samarov Nonparametric estimation of global functionals and a measure of the explanatory power of covariates in regression Ann. Statist. 23 1995 1443 1473
12. J Fan T.-C Hu Y.K Truong Robust non-parametric function estimation Scand. J. Statist. 21 1994 433 446
13. J.H Friedman Multivariate adaptive regression splines (with discussion) Ann. Statist. 19 1991 1 141
14. J.H Friedman B.W Silverman Flexible parsimonious smoothing and additive modeling Technometrics 31 1989 3 39
15. Friedman, J.H., Stuetzle, W., 1984. A variable-span smoother. Technical Report No. 5. Department of Statistics, Stanford University.
16. X He P Shi Convergence rate of B-spline estimators of nonparametric conditional quantile functions J. Nonparam. Statist. 3 1994 299 308
17. X He P Shi Bivariate tensor-product B-splines in a partially linear model J. Multivariate Anal. 58 1996 162 181
18. W Hendricks R Koenker Hierarchical spline models for conditional quantiles and the demand for electricity J. Amer. Statist. Assoc. 87 1992 58 68
19. R Koenker G Bassett Regression quantiles Econometrica 46 1978 33 50
20. R Koenker V D'Orey Computing regression quantiles Appl. Statist. 36 1987 383 392
21. R Koenker P Ng S Portnoy Quantile smoothing splines Biometrika 81 1994 673 680
22. Koo, J.-Y., 1997. Spline estimation of discontinuous regression functions. J. Comput. Graph. Statist., to appear.
23. C Kooperberg C.J Stone Y.K Truong Hazard regression J. Amer. Statist. Assoc. 90 1995 78 94
24. G.P Nason B.W Silverman The discrete wavelet transform in S J. Comput. Graph. Statist. 3 1994 163 191
25. 1 regression OR Spektrum 5 1983 229 239
26. W.H Press S.A Teukolsky W.T Vetterling B.P Flannery Numerical Recipes in Fortran: the Art of Scientific Computing 2nd Edition 1992 Cambridge University Press New York
27. G Schwarz Estimating the dimension of a model Ann. Statist. 6 1978 461 464
28. Y.K Truong Asymptotic properties kernel estimators based on local medians Ann. Statist. 17 1989 606 617