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Bandwidth Selection for Local Smoothing Jump Detector

Park, Dong-Ryeon    (Department of Information and Statistics, Hanshin University  );
  • 초록

    Local smoothing jump detection procedure is a popular method for detecting jump locations and the performance of the jump detector heavily depends on the choice of the bandwidth. However, little work has been done on this issue. In this paper, we propose the bootstrap bandwidth selection method which can be used for any kernel-based or local polynomial-based jump detector. The proposed bandwidth selection method is fully data-adaptive and its performance is evaluated through a simulation study and a real data example.


  • 주제어

    Bandwidth .   bootstrap .   discontinuous regression .   local smoothing jump detection.  

  • 참고문헌 (13)

    1. 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 
    2. Gijbels, I., Hall, P. and Kneip, A. (1999). On the estimation of jump points in smooth curves, Annals of the Institute of Statistical Mathematics, 51, 231?251 
    3. Gijbels, I. and Goderniaux, A. C. (2004). Bandwidth selection for change point estimation in nonparametric regression, Technometics, 46, 76?86 
    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 
    5. M$\ddot{u}$ller, H. G. (1992). Change-points in nonparametric regression analysis, The Annals of Statistics, 20, 737?761 
    6. Park, D. (2008). Estimation of jump points in nonparametric regression, Communications of the Korean Statistical Society, 15, 899?908     
    7. Park, D. (2009). Comparison of finite sample properties of jump detectors, Unpublished manuscript 
    8. Polzehl, 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 
    9. Qiu, P. (2003). A jump-preserving curve fitting procedure based on local piecewise-linear kernel estimation, Journal of Nonparametric Statistics, 15, 437?453 
    10. Qiu, P. (2005). Image Processing and Jump Regression Analysis, John Wiley & Sons, New Jersey 
    11. Qiu, P., Asano, C. and Li, X. (1991). Estimation of jump regression functions, Bulletin of Informatics and Cybernetics, 24, 197?212 
    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 
    13. Wu, J. S. and Chu, C. K. (1993). Kernel-type estimators of jump points and values of a regression function, The Annals of Statistics, 21, 1545?1566 
  • 이 논문을 인용한 문헌 (1)

    1. 2012. "" 한국통계학회 논문집 = Communications of the Korean Statistical Society, 19(4): 579~590     

 저자의 다른 논문

  • Park, Dong-Ryeon (12)

    1. 1997 "Choosing Optimal Design Points in Two Dimensional Space using Voronoi Tessellation" 한국통계학회 논문집 = Communications of the Korean Statistical Society 4 (1): 129~138    
    2. 2000 "Robust Nonparametric Regression Method using Rank Transformation" 한국통계학회 논문집 = Communications of the Korean Statistical Society 7 (2): 575~583    
    3. 2002 "Optimal Design for Locally Weighted Quasi-Likelihood Response Curve Estimator" 한국통계학회 논문집 = Communications of the Korean Statistical Society 9 (3): 743~752    
    4. 2004 "Robust Estimator of Location Parameter" 한국통계학회 논문집 = Communications of the Korean Statistical Society 11 (1): 153~160    
    5. 2005 "Robust Cross Validation Score" 한국통계학회 논문집 = Communications of the Korean Statistical Society 12 (2): 413~423    
    6. 2006 "Monotone Local Linear Quasi-Likelihood Response Curve Estimates" 한국통계학회 논문집 = Communications of the Korean Statistical Society 13 (2): 273~283    
    7. 2008 "Estimation of Jump Points in Nonparametric Regression" 한국통계학회 논문집 = Communications of the Korean Statistical Society 15 (6): 899~908    
    8. 2008 "Test for Discontinuities in Nonparametric Regression" 한국통계학회 논문집 = Communications of the Korean Statistical Society 15 (5): 709~717    
    9. 2009 "Comparison of Jump-Preserving Smoothing and Smoothing Based on Jump Detector" 한국통계학회 논문집 = Communications of the Korean Statistical Society 16 (3): 519~528    
    10. 2010 "Comparison of Nonparametric Function Estimation Methods for Discontinuous Regression Functions" 응용통계연구 = The Korean journal of applied statistics 23 (6): 1245~1253    

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