On automatic boundary corrections

Annals of Statistics

Volumn 25, Issue 4, 1997, Pages 1691-1708

  Cheng, Ming Yen ^b   Fan, Jianqing ^a   Marron, J S ^a  

^a University of North Carolina at Chapel Hill   (United States)

^b NONE

Author keywords

Boundary correction; Data binning; Local polynomial fit; Minimax risk; Weak minimaxity

Indexed keywords

EID: 0031483680     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1031594737     Document Type: Article

References (34)

1. BROWN, L. D. and LOW, M. G. (1996). Asymptotic equivalence of nonparametric regression and white noise. Ann. Statist. 24 2384-2398.
2. BROWN, L., LOW, M. and ZHAO, L. (1997). Anomalous behavior of fixed parameter asymptotic rates of convergence in nonparametric function estimation problems. Unpublished manuscript.
3. CHENG, M. Y. (1994). On boundary effects of smooth curve estimators. Ph.D. dissertation, Dept. Statistics, Univ. North Carolina, Chapel Hill.
4. CHENG, M. Y. (1997). Boundary-aware estimators of integrated density derivative products. J. Roy. Statist. Soc. Ser. B 59 191-203.
5. CHENG, M. Y., FAN, J. and MARRON, J. S. (1993). Minimax efficiency of local polynomial fit estimators at boundaries. Mimeo Series 2098, Inst. Statist., Univ. North Carolina, Chapel Hill.
6. CHU, C. K. and MARRON, J. S. (1991). Choosing a kernel regression estimator. Statist. Sci. 6 404-436.
7. DJOJOSUGITO, R. A. and SPECKMAN, P. L. (1992). Boundary bias correction in nonparametric density estimation. Comm. Statist. Theory Methods 21 69-88.
8. DONOHO, D. L. and JOHNSTONE, I. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika 81 425-455.
9. DONOHO, D. L. and LIU, R. C. (1991). Geometrizing rate of convergence III. Ann. Statist. 19 668-701.
10. DONOHO, D. L., LIU, R. C. and MACGIBBON, B. (1990). Minimax risk over hyper rectangles, implications. Ann. Statist. 18 1416-1437.
11. EFROIMOVICH, S. (1996). On nonparametric regression for i.i.d. observations in general setting. Ann. Statist. 24 1126-1144.
12. EPANECHNIKOV, V. A. (1969). Nonparametric estimation of a multi dimensional probability density. Theory Probab. Appl. 14 153-158.
13. EUBANK, R. L. and SPECKMAN, P. (1991). A bias reduction theorem with applications in nonparametric regression. Scand. J. Statist. 18 211-222.
14. FAN, J. (1992). Design-adaptive nonparametric regression. J. Amer. Statist. Assoc. 87 998-1004.
15. FAN, J. (1993). Local linear regression smoothers and their minimax efficiency. Ann. Statist. 21 196-216.
16. FAN, J. and GIJBELS, I. (1992). Variable bandwidth and local linear regression smoothers. Ann. Statist. 20 2008-2036.
17. FAN, J. and HALL, P. (1994). On curve estimation by minimizing mean absolute deviation and its implications. Ann. Statist. 22 867-885.
18. FAN, J. and MARRON, J. S. (1994). Fast implementations of nonparametric curve estimators. J. Comput. Graph. Statist. 3 35-56.
19. FAN, J., GASSER, T., GIJBELS, I., BROCKMANN, M. and ENGELS, J. (1997). Local polynomial fitting: a standard for nonparametric regression. Ann. Inst. Statist. Math. 49 79-99.
20. GASSER, T. and MÜLLER, H. G. (1979). Kernel estimation of regression functions. Smoothing Techniques for Curve Estimation. Lecture Notes in Math. 757 23-68. Springer, New York.
21. GASSER, T., MÜLLER, H. G. and MAMMITZSCH, V. (1985). Kernels for nonparametric curve estimation. J. Roy. Statist. Soc. Ser. B 47 238-252.
22. GRANOVSKY, B. L. and MÜLLER, H. G. (1991). Optimizing kernel methods: a unifying variational principle. Internat. Statist. Rev. 59 373-388.
23. HALL, P. and WEHRLY, T. E. (1991). A geometrical method for removing edge effects from kernel-type nonparametric regression estimators. J. Amer. Statist. Assoc. 86 665-672.
24. HASTIE, T. and LOADER, C. (1993). Local regression: automatic kernel carpentry. Statist. Sci. 8 120-143.
25. JONES, M. C. (1993). Simple boundary correction for kernel density estimation. Statist. Comput. 3 135-146.
26. LEJEUNE, M. and SARDA, P. (1992). Smooth estimators of distribution and density functions. Comput. Statist. Data Anal. 14 457-471.
27. MÜLLER, H. G. (1991). Smooth optimal kernel estimators near endpoints. Biometrika 78 521-530.
28. 2. Ann. Statist. 13 984-997.
29. RICE, J. (1984). Boundary modification for kernel regression. Comm. Statist. Theory Methods 13 893-900.
30. RICE, J. and ROSENBLATT, M. (1981). Integrated mean squared error of a smoothing spline. J. Approx. Theory 33 353-365.
31. RUPPERT, D. and WAND, M. P. (1994). Multivariate weighted least squares regression. Ann. Statist. 22 1346-1370.
32. SACKS, J. and YLVISAKER, D. (1981). Asymptotically optimum kernels for density estimation at a point. Ann. Statist. 9 334-346.
33. SCHUSTER, E. F. (1985). Incorporating support constraints into nonparametric estimators of densities. Comm. Statist. Theory Methods 14 1123-1136.
34. STONE, C. J. (1977). Consistent nonparametric regression. Ann. Statist. 5 595-645.