A new kernel distribution function estimator based on a non-parametric transformation of the data

Scandinavian Journal of Statistics

Volumn 32, Issue 4, 2005, Pages 551-562

  Swanepoel, Jan W H ^a   Van Graan, Francois C ^a  

^a NORTH WEST UNIVERSITY   (South Africa)

Author keywords

Bias; Kernel distribution function estimator; Mean squared error; Non parametric transformation; Smoothed bootstrap; Survival analysis

Indexed keywords

EID: 28044445646     PISSN: 03036898     EISSN: 14679469     Source Type: Journal    
DOI: 10.1111/j.1467-9469.2005.00472.x     Document Type: Article

References (26)

1. Abdous, B. (1993). Note on the minimum mean integrated squared error of kernel estimates of a distribution function and its derivatives. Comm. Statist. Theory Methods 22, 603-609.
2. Abramson, I. S. (1982). On bandwidth variation in kernel estimates - a square root law. Ann. Statist. 10, 1217-1223.
3. Altman, N. & Léger, C. (1995). Bandwidth selection for kernel distribution function estimation. J. Statist. Plann. Inf. 46, 195-214.
4. Azzalini, A. (1981). A note on the estimation of a distribution function and quantiles by a kernel method. Biometrika 68, 326-328.
5. Bowman, A., Hall, P. & Prvan, T. (1998). Bandwidth selection for the smoothing of distribution functions. Biometrika 85, 799-808.
6. Degenhardt, H. J. A. (1993). Chung-Smirnov property for perturbed empirical distribution functions. Statist. Probab. Lett. 16, 97-101.
7. Falk, M. (1983). Relative efficiency and deficiency of kernel type estimators of smooth distribution functions. Statist. Neerl. 37, 73-83.
8. Hill, P. D. (1985). Kernel estimation of a distribution function. Comm. Statist. Theory Methods 14, 605-620.
9. Hössjer, O. & Ruppert, D. R. (1995). Asymptotics for the transformation kernel density estimator. Ann. Statist. 23, 1198-1222.
10. Jones, M. C. (1990). The performance of kernel density functions in kernel distribution function estimation. Statist. Probab. Lett. 9, 129-132.
11. Jones, M. C., Linton, O. & Nielsen, J. P. (1995). A simple bias reduction method for density estimation. Biometrika 82, 327-338.
12. Jones, M. C. & Signorini, D. F. (1997). A comparison of higher-order bias kernel density estimators. J. Amer. Statist. Assoc. 92, 1063-1073.
13. Nadaraya, E. A. (1964). Some new estimates for distribution functions. Theory Probab. Appl. 9, 497-500.
14. Reiss, R. D. (1981). Nonparametric estimation of smooth distribution functions. Scand. J. Statist. 8, 116-119.
15. Ruppert, D. R. & Cline, D. B. H. (1994). Bias reduction in kernel density estimation by smoothed empirical transformations. Ann. Statist. 22, 185-210.
16. Samiuddin, M. & El-Sayyad, G. M. (1990). On nonparametric kernel density estimates. Biometrika 77, 865-874.
17. Serfling, R. J. (1980). Approximation theorems of mathematical statistics. Wiley, New York, NY.
18. Shirahata, S. & Chu, I. S. (1992). Integrated squared error of kernel type estimator of distribution function. Ann. Inst. Statist. Math. 44, 579-591.
19. Singh, R. S., Gasser, T. & Prasad, B. (1983). Nonparametric estimates of distribution functions. Comm. Statist. Theory Methods 12, 2095-2108.
20. Silverman, B. W. (1986). Density estimation for statistics and data analysis. Chapman and Hall, London.
21. Swanepoel, J. W. H. (1988). Mean integrated squared error properties and optimal kernels when estimating a distribution function. Comm. Statist. Theory Methods 17, 3785-3799.
22. Watson, G. S. & Leadbetter, M. R. (1964). Hazard analysis II. Sankhyā Ser. A 26, 101-116.
23. Winter, B. B. (1973). Strong uniform consistency of integrals of density estimators. Can. J. Statist. 1, 247-253.
24. Winter, B. B. (1979). Convergence rate of perturbed empirical distribution functions. J. Appl. Probab. 16, 163-173.
25. Yamato, H. (1973). Uniform convergence of an estimator of a distribution function. Bull. Math. Statist. 15, 69-78.
26. Yukich, J. E. (1989). A note on limit theorems for perturbed empirical processes. Stochastic Process Appl. 33, 163-173.