Bootstrap Bandwidth Selection Methods for Local Linear Jump Detector

Park, Dong-Ryeon

  • Received : 2012.04.02
  • Accepted : 2012.06.20
  • Published : 2012.07.31


Local linear jump detection in a discontinuous regression function involves the choice of the bandwidth and the performance of a local linear jump detector depends heavily on the choice of the bandwidth. However, little attention has been paid to this important issue. In this paper we propose two fully data adaptive bandwidth selection methods for a local linear jump detector. The performance of the proposed methods are investigated through a simulation study.


Bandwidth for jump detector;bootstrap;local linear jump detector


  1. Gijbels, I. and Goderniaux, A. C. (2004). Bandwidth selection for change point estimation in nonparametric regression, Technometics, 46, 76-86.
  2. Gijbels, I., Hall, P. and Kneip, A. (1999). On the estimation of jump points in smooth curves, The Annals of the Institute of Statistical Mathematics, 51, 231-251.
  3. 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.
  4. Park, D. (2009a). Comparison of jump-preserving smoothing and smoothing based on jump detector, Communications of the Korean Statistical Society, 16, 519-528.
  5. Park, D. (2009b). Bandwidth selection for local smoothing jump detector, Communications of the Korean Statistical Society, 16, 1047-1054.
  6. Qiu, P. (2005). Image Processing and Jump Regression Analysis, John Wiley & Sons, New Jersey.
  7. Scott, D. W. (1992). Multivariate Density Estimation: Theory, Practice and Visualization, Wiley-Interscience, New York.
  8. Zhang, B., Su, Z. and Qiu, P. (2009). On jump detection in regression curves using local polynomial kernel estimation, Pakistan Journal of Statistics, 25, 505-528.
  9. 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.


Supported by : Hanshin University