On Pseudodata Methods for Removing Boundary Effects in Kernel Density Estimation

Journal of the Royal Statistical Society. Series B: Methodological

Volumn 58, Issue 3, 1996, Pages 551-563

  Cowling, Ann ^a,b   Hall, Peter ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b CSIRO   (Australia)

Author keywords

bias; boundary effects; boundary kernel; cross validation; density estimation; edge effects; intensity; kernel; order statistics; point processes; pseudodata; variance

Indexed keywords

EID: 33749896776     PISSN: 00359246     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.2517-6161.1996.tb02100.x     Document Type: Article

References (20)

1. Barnard, G. A. (1953) Time intervals between accidents — a note on Maguire, Pearson and Wynn's paper. Biometrika, 40, 212–213.
2. Boneva, L. I., Kendall, D. and Stefanov, I. (1971) Spline transformations: three new diagnostic aids for the statistical data-analyst (with discussion). J. R. Statist. Soc. B, 33, 1–70.
3. Cline, D. B. H. and Hart, J. D. (1991) Kernel estimation of densities with discontinuities or discontinuous derivative. Statistics, 22, 69–84.
4. Cowling, A. (1995) Some problems in kernel curve estimation. PhD Thesis. Australian National University, Canberra.
5. Cowling, A., Hall, P. and Phillips, M. J. (1995) Bootstrap confidence regions for the intensity of a Poisson point process. Submitted to J. Am. Statist. Ass.
6. Cox, D. R. and Lewis, P. A. W. (1966) The Statistical Analysis of Series of Events. London: Methuen.
7. David, H. A. (1981) Order Statistics, 2nd edn. New York: Wiley.
8. Diggle, P. and Marron, J. S. (1988) Equivalence of smoothing parameter selectors in density and intensity estimation. J. Am. Statist. Ass., 83, 793–800.
9. Gasser, T. and Müller, H. G. (1979) Kernel estimation of regression functions. Lect. Notes Math., 757, 23–68.
10. Gasser, T., Müller, H. G. and Mammitzsch, V. (1985) Kernels for nonparametric curve estimation. J. R. Statist. Soc. B, 47, 238–252.
11. Hall, P. and Wehrly, T. (1991) A geometrical method for removing edge effects from kernel-type nonparametric regression estimators. J. Am. Statist. Ass., 86, 665–672.
12. Jarrett, R. G. (1979) A note on the intervals between coal-mining disasters. Biometrika, 66, 191–193.
13. Maguire, B. A., Pearson, E. S. and Wynn, A. H. A. (1952) The time intervals between industrial events. Biometrika, 39, 168–180.
14. Müller, H. G. (1984) Boundary effects in nonparametric curve estimation models. In Compstat 1984 (eds T. Havranek, A. Sidak and M. Novak), pp. 84–89. Vienna: Physica.
15. Müller, H. G. (1988) Nonparametric regression analysis of longitudinal data. Lect. Notes Statist., 46.
16. Rice, J. (1984) Boundary modification for kernel regression. Communs Statist. Theory Meth., 13, 893–900.
17. Rice, J. and Rosenblatt, M. (1983) Smoothing splines: regression, derivatives, and deconvolution. Ann. Statist., 11, 141–156.
18. Schuster, E. F. (1985) Incorporating support constraints into nonparametric estimation of densities. Communs Statist. Theory Meth., 14, 1123–1136.
19. Scott, D. W., Tapia, R. A. and Thompson, J. R. (1977) Kernel density estimation revisited. Nonlin. Anal. Theory Meth. Applic., 1, 339–372.
20. Silverman, B. W. (1986) Density Estimation for Statistics and Data Analysis. London: Chapman and Hall.