A generalized reflection method of boundary correction in kernel density estimation

Canadian Journal of Statistics

Volumn 33, Issue 4, 2005, Pages 497-509

  Karunamuni, Rohana J ^a   Alberts, Tom ^b  

^a UNIVERSITY OF ALBERTA   (Canada)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

Density estimation; Kernel estimation; Mean squared error; Reflection

Indexed keywords

EID: 33644682974     PISSN: 03195724     EISSN: None     Source Type: Journal    
DOI: 10.1002/cjs.5550330403     Document Type: Article

References (22)

1. M. Y. Cheng (1997). Boundary-aware estimators of integrated density derivative. Journal of the Royal Statistical Society Series B, 59, 191-203.
2. D. B. H. Cline & J. D. Hart (1991). Kernel estimation of densities of discontinuous derivatives. Statistics, 22, 69-84.
3. A. Cowling & P. Hall (1996). On pseudodata methods for removing boundary effects in kernel density estimation. Journal of the Royal Statistical Society Series B, 58, 551-563.
4. 1 View. Wiley, New York.
5. T. Gasser & H. G. Müller (1979). Kernel estimation of regression functions. In Smoothing Techniques for Curve Estimation (T. Gasser & M. Rosenblatt, eds.), Lecture Notes in Mathematics 757, Springer, New York, pp. 23-68.
6. T. Gasser, H. G. Müller & V. Mammitzsch (1985). Kernels for nonparametric curve estimation. Journal of the Royal Statistical Society Series B, 47, 238-252.
7. P. Hall & B. U. Park (2002). New methods for bias correction at endpoints and boundaries. The Annals of Statistics, 30, 1460-1479.
8. N. L. Hjort & M. C. Jones (1996). Locally parametric nonparametric density estimation. The Annals of Statistics, 24, 1619-1647.
9. M. C. Jones (1993). Simple boundary correction for kernel density estimation. Statistics & Computing, 3, 135-146.
10. M. C. Jones & P. J. Foster (1996). A simple nonnegative boundary correction method for kernel density estimation. Statistica Sinica, 6, 1005-1013.
11. R. J. Karunamuni & T. Alberts (2003). A locally adaptive generalized reflection method of boundary correction in kernel density estimation. Technical report.
12. C. R. Loader (1996). Local likelihood density estimation. The Annals of Statistics, 24, 1602-1618.
13. J. S. Marron & D. Ruppert (1994). Transformations to reduce boundary bias in kernel density estimation. Journal of the Royal Statistical Society Series B, 56, 653-671.
14. H. G. Müller (1991). Smooth optimum kernel estimators near endpoints. Biometrika, 78, 521-530.
15. E. Parzen (1962). On estimation of a probability density function and mode. The Annals of Mathematical Statistics, 33, 1065-1076.
16. B. L. S. Prakasa Rao (1983). Nonparametric Functional Estimation. Academic Press, Orlando, Florida.
17. B. W. Silverman (1986). Density Estimation for Statistics and Data Analysis. Chapman & Hall, London.
18. M. P. Wand & M. C. Jones (1995). Kernel Smoothing. Chapman & Hall, London.
19. M. P. Wand, J. S. Marron & D. Ruppert (1991). Transformations in density estimation (with discussion). Journal of the American Statistical Association, 86, 343-361.
20. S. Zhang & R. J. Karunamuni (1998). On kernel density estimation near endpoints. Journal of Statistical Planning and Inference, 70, 301-316.
21. S. Zhang & R. J. Karunamuni (2000). On nonparametric density estimation at the boundary. Nonparametric Statistics, 12, 197-221.
22. S. Zhang, R. J. Karunamuni & M. C. Jones (1999). An improved estimator of the density function at the boundary. Journal of the American Statistical Association, 448, 1231-1241.