Communications for Statistical Applications and Methods

  • 제16권3호
  • /
  • Pages.519-528
  • /
  • 2009
  • /
  • 2287-7843(pISSN)
  • /
  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

Comparison of Jump-Preserving Smoothing and Smoothing Based on Jump Detector

  • 발행 : 2009.05.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

This paper deals with nonparametric estimation of discontinuous regression curve. Quite number of researches about this topic have been done. These researches are classified into two categories, the indirect approach and direct approach. The major goal of the indirect approach is to obtain good estimates of jump locations, whereas the major goal of the direct approach is to obtain overall good estimate of the regression curve. Thus it seems that two approaches are quite different in nature, so people say that the comparison of two approaches does not make much sense. Therefore, a thorough comparison of them is lacking. However, even though the main issue of the indirect approach is the estimation of jump locations, it is too obvious that we have an estimate of regression curve as the subsidiary result. The point is whether the subsidiary result of the indirect approach is as good as the main result of the direct approach. The performance of two approaches is compared through a simulation study and it turns out that the indirect approach is a very competitive tool for estimating discontinuous regression curve itself.

키워드

참고문헌

  1. Bowman, A. W., Pope, A. B. and Ismail, B. (2006). Detecting discontinuities in nonparametric reg-ression curves and surfaces, Statistics and Computing, 16, 377-390 https://doi.org/10.1007/s11222-006-9618-y
  2. Burt, D. A. (2000). Bandwidth selection conderns for jump point discontinuity preservation in the regression setting using M-smoothers and the extension to hypothesis testing, Ph. D. dissertation, Virginia Polytechnic Institute and State University, Department of Statistics
  3. Chu, C. K., Glad. I. K., Godtliebsen, F. and Marron, J. S. (1998). Edge preserving smoothers for image processing (with discussion), Journal of the American Statistical Association, 93, 526-556 https://doi.org/10.2307/2670100
  4. Gijbels, I., Lambert, A. and Qiu, P. (2007). Jump-preserving regression and smoothing using local linear fitting: A compromise, Annals of the Institute of Statistical Mathematics, 59, 235-272 https://doi.org/10.1007/s10463-006-0045-9
  5. Gijbels, I. and Goderniaux, A. C. (2004). Bandwidth selection for change point estimation in non-parametric regression, Technometics, 46, 76-86 https://doi.org/10.1198/004017004000000130
  6. Hall, P. and Titterington, D. M. (1992). Edge-preserving and peak-preserving smoothing. Technomet-ics, 34, 429-440 https://doi.org/10.2307/1268942
  7. Muller, H. G. (1992). Change-points in nonparametric regression analysis, The Annals of Statistics, 20, 737-761 https://doi.org/10.1214/aos/1176348654
  8. Park, D. (2008). Estimation of jump points in nonparametric regression, Communications of the Korean Statistical Society, 15, 899-908 https://doi.org/10.5351/CKSS.2008.15.6.899
  9. Polzehi, J. and Spokoiny, V. G. (2000). Adaptive weights smoothing with applications to image restoration, Journal of the Royal Statistical Society: Series B, 62, 335-354 https://doi.org/10.1111/1467-9868.00235
  10. Qiu, P. (2003). A jump-preserving curve fitting procedure based on local piecewise-linear kernel estimation, Journal of Nonparametric Statistics, 15, 437-453 https://doi.org/10.1080/10485250310001595083
  11. Qiu, P. and Yandell, B. (1998). A local polynomial jump detection algorithm in nonparametric regres-sion, Technometrics, 40, 141-152 https://doi.org/10.2307/1270648
  12. Rue, H., Chu. C. K., Godtliebsen, F. and Marron, J. S. (2002). M-smoother with local linear fit, Journal of Nonparametric Statistics, 14, 155-168 https://doi.org/10.1080/10485250211385
  13. Simpson, D. G., He, X. and Liu, Y. (1998). Comment on: Edge-preserving smoothers for image, In Processing Journal of the American Statistical Association, 93, 544-548 https://doi.org/10.2307/2670102
  14. Wu, J. S. and Chu, C. K. (1993a). Kernel-type estimators of jump points and values of a regression function, The Annals of Statistics, 21, 1545-1566 https://doi.org/10.1214/aos/1176349271
  15. Wu, J. S. and Chu, C. K. (1993b). Nonparametric function estimation and bandwidth selection for discontinuous regression functions, Statistica Sinica, 3, 557-576

피인용 문헌

  1. Bootstrap Bandwidth Selection Methods for Local Linear Jump Detector vol.19, pp.4, 2012, https://doi.org/10.5351/CKSS.2012.19.4.579
  2. Comparison of Nonparametric Function Estimation Methods for Discontinuous Regression Functions vol.23, pp.6, 2010, https://doi.org/10.5351/KJAS.2010.23.6.1245