Estimation of Jump Points in Nonparametric Regression

  • Published : 2008.11.30


If the regression function has jump points, nonparametric estimation method based on local smoothing is not statistically consistent. Therefore, when we estimate regression function, it is quite important to know whether it is reasonable to assume that regression function is continuous. If the regression function appears to have jump points, then we should estimate first the location of jump points. In this paper, we propose a procedure which can do both the testing hypothesis of discontinuity of regression function and the estimation of the number and the location of jump points simultaneously. The performance of the proposed method is evaluated through a simulation study. We also apply the procedure to real data sets as examples.


  1. Bowman, A. W., Pope, A. and Ismail, B. (2006). Detecting discontinuities in nonparametric regression curves and surfaces, Statistics & Computing, 16, 377-390
  2. Gijbels, I. and Goderniaux, A. C. (2004). Bandwidth selection for change point estimation in nonparametric regression, Technometrics, 46, 76-86
  3. Hall, P. and Titterington, D. M. (1992). Edge-preserving and peak-preserving smoothing, Technometics, 34, 429-440
  4. Muller, H. G. (1992). Change-points in nonparametric regression analysis, The Annals of Statistics, 20, 737-761
  5. Muller, H. G. and Stadtmuller, U. (1999). Discontinuous versus smooth regression, The Annals of Statistics, 27, 299-337
  6. Park, D. (2008). Test for discontinuities in nonparametric regression, To appear in Communications of the Korean Statistical Society
  7. Qiu, P. (1994). Estimation of the number of jumps of the jump regression functions, Communications in Statistics-Theory and Methods, 23, 2141-2155
  8. Qiu, P. (2005). Image Processing and Jump Regression Analysis, John Wiley & Sons, New Jersey
  9. Qiu, P., Asano, Chi. and Li, X. (1991). Estimation of jump regression functions, Bulletin of Informatics and Cybernetics, 24, 197-212
  10. Qiu, P. and Yandell, B. (1998). A local polynomial jump detection algorithm in nonparametric regression, Technometrics, 40, 141-152
  11. Scott, D. W. (1992). Multivariate Density Estimation: Theory, Practice and Visualization, Wiley-Interscience, New York
  12. 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

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