The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

On the Selection of Bezier Points in Bezier Curve Smoothing

  • Kim, Choongrak (Department of Statistics, Pusan National University) ;
  • Park, Jin-Hee (Department of Statistics, Pusan National University)
  • Received : 2012.10.11
  • Accepted : 2012.11.15
  • Published : 2012.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

Nonparametric methods are often used as an alternative to parametric methods to estimate density function and regression function. In this paper we consider improved methods to select the Bezier points in Bezier curve smoothing that is shown to have the same asymptotic properties as the kernel methods. We show that the proposed methods are better than the existing methods through numerical studies.

Keywords

References

  1. Bae, W., Choi, H., Park, B.-U. and Kim, C. (2005). Smoothing techniques for the bivariate Kaplan-Meier estimator, Communications in Statistics - Theory and Methods, 34, 1659-1674. https://doi.org/10.1081/STA-200063317
  2. Bezier, P. (1977). Essay de Definition Numerique des Courbes et des Surfaces Experimentals. Ph.D. thesis, University of Paris VI.
  3. Eubank, R. L. (1988). Spline Smoothing and Nonparametric Regression, Marcel Dekker, New York.
  4. Fan, J. and Gijbels, I. (1996). Local Polynomial Modelling and Its Applications, Chapman and Hall, London.
  5. Farin, G. E. (1990). Curves and Surfaces for Computer Aided Geometric Design, Academic Press Inc, London.
  6. Kim, C. (1996). Nonparametric density estimation via the Bezier curve, ASA Proceedings of the Section on Statistical Graphics, 25-28.
  7. Kim, C., Hong, C. and Jeong, M. (2000). Simulation-Extrapolation via the Bezier curve in measurement error models, Communications in Statistics - Simulation and Computation, 29, 1135-1147. https://doi.org/10.1080/03610910008813657
  8. Kim, C., Kim, W., Hong, C., Park, B.-U. and Jeong, M. (1999). Smoothing techniques via the Bezier curve, Communications in Statistics - Theory and Methods, 28, 1577-1596. https://doi.org/10.1080/03610929908832374
  9. Kim, C., Kim, W., Park, B.-U. and Lim, J. (2003). Bezier curve smoothing of the Kaplan-Meier estimator, Annals of the Institute of Statistical Mathematics, 55, 359-367.
  10. Linhart, H. and Zucchini, W. (1986). Model Selection, Wiley, New York.
  11. Loader, C. (1999). Local Regression and Likelihood, Springer, London.
  12. Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis, Chapman and Hall, New York.
  13. Wand, M. P. and Jones, M. C. (1995). Kernel Smoothing, Chapman and Hall, London.
  14. Wasserman, L. (2006). All of Nonparametric Statistics, Springer, London.

Cited by

  1. Bezier curve smoothing of cumulative hazard function estimators vol.23, pp.3, 2016, https://doi.org/10.5351/CSAM.2016.23.3.189
  2. Nonparametric Estimation of Distribution Function using Bezier Curve vol.21, pp.1, 2014, https://doi.org/10.5351/CSAM.2014.21.1.105