On the asymptotics of penalized splines

Biometrika

Volumn 95, Issue 2, 2008, Pages 415-436

  Li, Yingxing ^a   Ruppert, David ^b  

^a Department of Obstetrics Gynecology   (United States)

^b Cornell University   (United States)

Author keywords

Asymptotic bias; B spline; Binning; Difference penalty; Equivalent kernel; Increasing number of knots; P spline

Indexed keywords

EID: 44849098150     PISSN: 00063444     EISSN: 14643510     Source Type: Journal    
DOI: 10.1093/biomet/asn010     Document Type: Article

References (18)

1. AGARWAL, G. G. & STUDDEN, W. J. (1980). Asymptotic integrated mean square error using least squares and bias minimizing splines. Ann. Statist. 8, 1307-25.
2. DOW, M. (2003). Explicit inverses of Toeplitz and associated matrices. ANZIAM J. 44, E185-E215.
3. EILERS, P. H. C. & MARX, B. D. (1996). Flexible smoothing with B-splines and penalties (with Discussion). Statist. Sci. 11, 89-121.
4. ELAYDI, S. (2005). An Introduction to Difference Equations. New York: Springer.
5. FAN, J. (1992). Design-adaptive nonparametric regression. J. Am. Statist. Assoc. 87, 998-1004.
6. GRADSHTEYN, I. & RYZHIK, I. (1980). Table of Integrals, Series, and Products. New York: Academic Press.
7. HALL, P. & OPSOMER, J. D. (2005). Theory for penalized spline regression. Biometrika 92, 105-18.
8. HALL, P. & WAND, M. P. (1996). On the accuracy of binned kernel density estimators. J. Mult. Anal. 5, 165-84.
9. O'SULLIVAN, F. (1986). A statistical perspective on ill-posed inverse problems (with Discussion). Statist. Sci. 1, 505-27.
10. RUPPERT, D. (2002). Selecting the number of knots for penalized splines. J. Comp. Graph. Statist. 11, 735-57.
11. RUPPERT, D. & WAND, M. P. (1994). Multivariate locally weighted least squares regression. Ann. Statist. 22, 1346-69.
12. RUPPERT, D., WAND, M. P. & CARROLL, R. J. (2003). Semiparametric Regression. Cambridge: Cambridge University Press.
13. SILVERMAN, B. W. (1984). Spline smoothing: the equivalent variable kernel method. Ann. Statist. 12, 898-916.
14. STUTE, W. (1982). The oscillation behavior of empirical processes. Ann. Prob. 10, 86-107.
15. STUTE, W. (1984). Asymptotic normality of nearest neighbor regression function estimates. Ann. Statist. 12, 917-26.
16. WAND, M. P. (1999). On the optimal amount of smoothing in penalized spline regression. Biometrika 86, 936-40.
17. WAND, M. P. & JONES, M. C. (1995). Kernel Smoothing. London: Chapman & Hall/CRC.
18. YU, Y. & RUPPERT, D. (2002). Penalized spline estimation for partially linear single index model. J. Am. Statist. Assoc. 97, 1042-54.