Browse > Article
http://dx.doi.org/10.5351/CKSS.2009.16.3.519

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

Park, Dong-Ryeon (Department of Statistics, Hanshin University)
Publication Information
Communications for Statistical Applications and Methods / v.16, no.3, 2009 , pp. 519-528 More about this Journal
Abstract
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.
Keywords
Difference Kernel estimators; discontinuous regression function; lump detector; jump-preserving smoothing; local constant M-smoother;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 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   DOI   ScienceOn
2 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   DOI   ScienceOn
3 Wu, J. S. and Chu, C. K. (1993b). Nonparametric function estimation and bandwidth selection for discontinuous regression functions, Statistica Sinica, 3, 557-576
4 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   DOI   ScienceOn
5 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   DOI
6 Gijbels, I. and Goderniaux, A. C. (2004). Bandwidth selection for change point estimation in non-parametric regression, Technometics, 46, 76-86   DOI   ScienceOn
7 Hall, P. and Titterington, D. M. (1992). Edge-preserving and peak-preserving smoothing. Technomet-ics, 34, 429-440   DOI
8 Muller, H. G. (1992). Change-points in nonparametric regression analysis, The Annals of Statistics, 20, 737-761   DOI
9 Park, D. (2008). Estimation of jump points in nonparametric regression, Communications of the Korean Statistical Society, 15, 899-908   과학기술학회마을   DOI   ScienceOn
10 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   DOI   ScienceOn
11 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
12 Qiu, P. (2003). A jump-preserving curve fitting procedure based on local piecewise-linear kernel estimation, Journal of Nonparametric Statistics, 15, 437-453   DOI   ScienceOn
13 Qiu, P. and Yandell, B. (1998). A local polynomial jump detection algorithm in nonparametric regres-sion, Technometrics, 40, 141-152   DOI
14 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   DOI   ScienceOn
15 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   DOI