Bernstein polynomial probability density estimation

Journal of Nonparametric Statistics

Volumn 16, Issue 5, 2004, Pages 709-729

  Kakizawa, Yoshihide ^a  

^a HOKKAIDO UNIVERSITY   (Japan)

Author keywords

Bernstein polynomial; Boundary bias; Kernel estimate; Mean integrated squared error (MISE); Probability density function

Indexed keywords

EID: 3042687240     PISSN: 10485252     EISSN: None     Source Type: Journal    
DOI: 10.1080/1048525042000191486     Document Type: Article

References (19)

1. Babu, G. J., Canty, A. J. and Chaubey, Y. P. (2002). Application of Bernstein polynomials for smooth estimation of a distribution and density function. Journal of Statistical Planning and Inference, 105, 377-392.
2. Bartlett, M. S. (1963). Statistical estimation of density functions. Sankhyā A, 25, 245-254.
3. Chen, S. X. (1996). Empirical likelihood confidence intervals for nonparametric density estimation. Biometrika. 83, 329-341.
4. Chen, S. X. (1999). Beta kernel estimators for density functions. Computational Statistics & Data Analysis, 31, 131-145.
5. Chen, S. X. (2000). Beta kernel smoothers for regression curves. Statistica Sinica, 10, 73-91.
6. Feller, W. (1997). An Introduction To Probability Theory and Its Applications, Vol. II, 2nd ed., Wiley. New York.
7. Gasser, T. and Müller, H. G. (1979). Kernel estimation of regression functions. In: Gasser, T. and Rosenblatt, M. (Eds.), Smoothing Techniques for Curve Estimation. Springer, Berlin, pp. 23-68.
8. Gasser, T., Müller, H. G. and Mammitzsch, V. (1985). Kernels for nonparametric curve estimation. Journal of the Royal Statistical Society B. 47, 238-252.
9. Gawronski, W. and StadtMüller, U. (1981). Smoothing histograms by means of lattice- and continuous distributions. Metrika, 28, 155-164.
10. Ghosal, S. (2001). Convergence rates for density estimation with Bernstein polynomials. The Annals of Statistics, 29, 1264-1280.
11. Jones, M. C. (1993). Simple boundary correction for kernel density estimation. Statistics and Computing, 3, 135-146.
12. Müller, H. G. (1988). Nonparametric Regression Analysis of Longitudinal Data. Springer. Berlin.
13. Müller, H. G. (1991). Smooth optimum kernel estimators near endpoints. Biometrika, 78, 521-530.
14. Parzen, E. (1962). On estimation of probability density and mode. The Annals of Mathematical Statistics, 33, 1065-1070.
15. Rosenblatt, M. (1956). Remarks on some nonparametric estimates of density functions. The Annals of Mathematical Statistics, 27, 832-837.
16. Rosenblatt, M. (1971). Curve estimates. The Annals of Mathematical Statistics, 42, 1815-1842.
17. StadtMüller, U. (1983). Asymptotic distributions of smoothed histograms. Metrika, 30, 145-158.
18. Vitale, R. A. (1975). A Bernstein polynomial approach to density function estimation. In: Puri, M. L. (Ed.), Statistical Inference and Related Topics, Vol. 2, Academic Press, New York, pp. 87-99.
19. Wand, M. P. and Jones, M. C. (1995). Kernel Smoothing. Chapman & Hall, London.