Nonparametric Discontinuity Point Estimation in Density or Density Derivatives

  • Huh, Jib (Department of Mathematics, Kyung Hee University)
  • Published : 2002.06.01

Abstract

Probability density or its derivatives may have a discontinuity/change point at an unknown location. We propose a method of estimating the location and the jump size of the discontinuity point based on kernel type density or density derivatives estimators with one-sided equivalent kernels. The rates of convergence of the proposed estimators are derived, and the finite-sample performances of the methods are illustrated by simulated examples.

Keywords

References

  1. Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete v.37 The minimum of an additive process with applications to signal estimation and storage theory Bhattacharya, P. K.;Brockwell, P. J.
  2. Convergence of Probability Measures Billingsley, P.
  3. Statistics v.22 Kernel estimation of densities with discontinuities or discontinuous derivatives Cline, D. B. H.;Hart, J. D.
  4. Local Polynomial Modelling and Its Application Fan, J.;Gijbels, I.
  5. manuscript Detection of change point with local polynomial fits for random design case Huh, J.;Park, B. U.
  6. The Annals of Statistics v.24 Change point estimation using nonparametric regression Loader, C. R.
  7. Journal of the American Statistical Association v.82 Weighted local regression and kernel methods for nonparametric curve fitting Muller, H. G.
  8. The Annals of Statistics v.20 Change-points in nonparametric regression analysis Muller, H. G.
  9. Biometrika v.77 Nonparametric analysis of changes in hazard rates for censored survival data: An alternative to change-point models Muller, H. G.;Wang, J. L.
  10. Communications in Statistics-Theory and Methods v.14 Incorporating support constraints into nonparametric estimators of densities Schuster, E. F.
  11. Kernel Smoothing Wand, M. P.;Jones, M. C.
  12. Annals of Mathematical Statistics v.41 Weak convergence of probability measures on the function space c([0,∞]) Whitt, W.