Boundary aware estimators of integrated density derivative products

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 59, Issue 1, 1997, Pages 191-203

  Cheng, Ming Yen ^a  

^a NATIONAL CHUNG CHENG UNIVERSITY   (Taiwan)

Author keywords

Bandwidth selection; Boundary effects; Data binning; Local polynomial fitting; Plug in bandwidth selector

Indexed keywords

EID: 0039016620     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9868.00063     Document Type: Article

References (20)

1. Aldershof, B. (1991) Estimation of integrated squared density derivatives. Mimeo 2053. Institute of Statistics, University of North Carolina, Chapel Hill.
2. Bickel, P. J. and Ritov, Y. (1988) Estimating integrated squared density derivatives: sharp best order of convergence estimates. Sankhya A, 50, 381-393.
3. Cheng, M.-Y. (1994) On boundary effects of smooth curve estimators. Mimeo 2319. Institute of Statistics, University of North Carolina, Chapel Hill.
4. _ (1995) A bandwidth selector for local linear density estimators. Ann. Statist., to be published.
5. Cheng, M.-Y., Fan, J. and Marron, J. S. (1995) On automatic boundary corrections. Submitted to Ann. Statist.
6. Fan, J., Gasser, T., Gijbels, I., Brockmann, M. and Engel, J. (1993) Local polynomial fitting: a standard for nonparametric regression. Mimeo 2302. Institute of Statistics, University of North Carolina, Chapel Hill.
7. Gasser, T., Müller, H.-G. and Mammitzsch, V. (1985) Kernels for nonparametric curve estimation. J. R. Statist. Soc. B, 47, 238-252.
8. Hall, P. and Marron, J, S. (1987) Estimation of integrated squared density derivatives. Statist. Probab. Lett., 6, 109-115.
9. Jones, M. C. (1993) Simple boundary correction for kernel density estimation. Statist. Comput., 3, 135-146.
10. Jones, M. C., Marron, J. S. and Sheather, S. J. (1994) Progress in data-based bandwidth selection for kernel density estimation. Mimeo 2088. Institute of Statistics, University of North Carolina, Chapel Hill.
11. Jones, M. C. and Sheather, S. J. (1991) Using non-stochastic terms to advantage in kernel-based estimation of integrated squared density derivatives. Statist. Probab. Lett., 11, 511-514.
12. Lejeune, M. (1984) Optimization in non-parametric regression. In COMPSTAT 1984 - Proc. 6th Symp. Computing in Statistics (eds T. Havranek, Z. Sidak and M. Novak), pp. 421-426. Heidelberg: Physica.
13. Lejeune, M. and Sarda, P. (1992) Smooth estimators of distribution and density functions. Comput. Statist. Data Anal., 14, 457-471.
14. Müller, H. G. (1987) Weighted local regression and kernel methods for nonparametric curve fitting. J. Am. Statist. Ass., 82, 231-238.
15. Ruppert, D., Sheather, S. J. and Wand, M. P. (1995) An effective bandwidth selector for local least squares regression. J. Am. Statist. Ass., 90, 1257-1270.
16. Ruppert, D. and Wand, M. P. (1994) Multivariate locally weighted least squares regression. Ann. Statist., 22, 1346-1370.
17. Sheather, S. J. (1992) The performance of six popular bandwidth selection methods on some real data sets. Comput. Statist., 7, 225-250.
18. Sheather, S. J. and Jones, M. C. (1991) A reliable data-based bandwidth selection method for kernel density estimation. J. R. Statist. Soc. B, 53, 683-690.
19. Stone, C. J. (1977) Consistent nonparametric regression. Ann. Statist., 5, 595-645.
20. Van Es, A. J. and Hoogstrate, A. J. (1994) Kernel estimators of integrated squared density derivatives in non-smooth cases. In Asymptotic Statistics: Proc. 5th Prague Symp. (eds P. Mandl and M. Hušková), pp. 313-224. Heidelberg: Physica.