On derivative estimation in spline regression

Statistica Sinica

Volumn 10, Issue 1, 2000, Pages 93-108

  Zhou, Shanggang ^a   Wolfe, Douglas A ^b  

^a KANSAS STATE UNIVERSITY   (United States)

^b NONE

Author keywords

Asymptotic bias; Asymptotic normality; Asymptotic variance; B splines; Bernoulli polynomial; Derivative estimators; Heteroscedastic errors; Random designs; Regression splines

Indexed keywords

EID: 0034383562     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. Agarwal, G. G. and Studden, W. J. (1980). Asymptotic integrated mean square error using least squares and bias minimizing splines. Ann. Statist. 8, 1307-1325.
2. 2 approximation by splines. Numer. Math. 33, 101-114.
3. Chu, C. K. and Marron, J. S. (1991). Choosing a kernel regression estimator (with discussion). Statist. Sci. 74, 829-836.
4. de Boor, C. (1972). On calculating with B-splines. J. Approx. Theor. 6, 50-62.
5. Eubank, R. L. and Speckman, P. L. (1993). Confidence bands in nonparametric regression. J. Amer. Statist. Assoc. 88, 1287-1301.
6. Friedman, J. H. (1991). Multivariate adaptive regression splines (with discussion). Ann. Statist. 19, 1-141.
7. Friedman, J. H. and Silverman, B. W. (1989). Flexible parsimonious smoothing and additive modeling (with discussion). Technometrics 31, 3-21.
8. Gaenssler, P. and Wellner, J. A. (1981). Glivenko-Cantelli Theorems. Encyclopedia of Statistical Science 3, 442-445.
9. Gasser, Th. and Müller, H. G. (1984). Estimating regression functions and their derivatives by the kernel method. Scand. J. Statist. 11, 171-185.
10. Ghizzetti, A. and Ossicini, A. (1970). Quadrature Formulae. Academic Press, New York.
11. Müller, H. G. (1988). Nonparametric Analysis of Longitudinal Data. Springer, Berlin.
12. Ortega, J. M. (1987). Matrix Theory. Plenum Press, New York.
13. Ruppert, D., Sheather, S. J. and Wand, M. P. (1995). An effective bandwidth selector for local least squares regression. J. Amer. Statist. Assoc. 90, 1257-1270.
14. Ruppert, D. and Wand, M. P. (1994). Multivariate locally weighted least squares regression. Ann. Statist. 22, 1346-1370.
15. Sacks, J. and Ylvisaker, D. (1970). Designs for regression problems with correlated errors III. Ann. Math. Statist. 41, 2057-2074.
16. Schumaker, L. L. (1981). Spline Functions: Basic Theory. Wiley, New York.
17. Stone, C. (1982). Optimal global rates of convergence for nonparametric regression. Ann. Statist. 10, 1040-1053.
18. Stone, C. (1985). Additive regression and other nonparametric models. Ann. Statist. 13, 689-705.
19. Stone, C. (1994). The use of polynomial splines and their tensor products in multivariate function estimation. Ann. Statist. 22, 118-184.
20. Stone, C. and Koo, C. Y. (1986). Additive splines in statistics. In Proceedings of the Statistical Computing Section, 45-48. Amer. Statist. Assoc., Washington, DC.
21. Zhou, S., Shen, X. and Wolfe, D. A. (1998). Local asymptotics for regression splines and confidence regions. Ann. Statist. 26, 1760-1782.