Large sample properties of shape restricted regression estimators with smoothness adjustments

Statistica Sinica

Volumn 17, Issue 4, 2007, Pages 1601-1616

  Pal, Jayanta Kumar ^a   Woodroofe, Michael ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Asymptotic normality; Green's function; Monotonic function; Smoothing spline

Indexed keywords

EID: 38549113694     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. Friedman, J. and Tibshirani, R. (1984). The monotone smoothing of scatterplots. Technometrics 26, 243-250.
2. Groeneboom, P. and Wellner, J. A. (2001). Computing Chernoff's distribution. J. Comput. Graph. Statist. 10, 388-400.
3. Hall, P. and Huang, L.-S. (2001). Nonparametric kernel regression subject to monotonicity constraints. Ann. Statist. 29, 624-647.
4. Mammen, E. (1991). Estimating a smooth monotone regression function. Ann. Statist. 19, 724-740.
5. Mammen, E., Marron, J. S., Turlach, B. A. and Wand, M. P. (2001). A general projection framework for constrained smoothing. Statist. Sci. 16, 232-248.
6. Messer, K. (1991). A comparison of a spline estimate to its equivalent kernel estimate. Ann. Statist. 19, 817-829.
7. Meyer, M. and Woodroofe, M. B. (2000). On the degrees of freedom of shape restricted regression. Ann. Statist. 28, 1083-1104.
8. Mukherjee, H. (1988). Monotone non-parametric regression. Ann. Statist. 16, 741-750.
9. Nychka, D. (1995). Splines as local smoothers. Ann. Statist. 23, 1175-1197.
10. Pal, J. and Woodroofe, M. B. (2004). On the distance between the Cumulative Sum Diagram and its Greatest Convex Minorant under unequally spaced design points. Scand. J. Statist. 33, 279-292.
11. Ramsay, J. O. (1998). Estimating smooth monotone functions. J. Roy. Statist. Soe. Ser. B 60, 365-375.
12. Rice, J. and Rosenblatt, M. (1983). Smoothing splines: regression, derivatives and deconvolution. Ann. Statist. 11, 141-156.
13. Robertson, T., Wright, F. T. and Dykstra, R. L. (1987). Order Restricted Statistical Inference. Wiley, New York.
14. Silverman, B. (1984). Spline smoothing: the equivalent variable kernel method. Ann. Statist. 12, 898-916.
15. Tantiyaswasdikul, C. and Woodroofe, M. B. (1994). Isotonic smoothing splines under sequential designs. J. Statist. Plann. Inference 38, 75-87.
16. Wright, F. T. (1981). The asymptotic behavior of monotone regression estimates. Ann. Statist. 9, 443-448.