On the distribution of the clipping median under a mixture model

Statistics and Probability Letters

Volumn 71, Issue 1, 2005, Pages 1-13

  Steland, Ansgar ^a  

^a RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

Change point; Econometrics; Edge detection; Image processing; Jump preserving estimation; Nonparametric regression; Robust statistics

Indexed keywords

EID: 27444448136     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2004.10.016     Document Type: Article

References (16)

1. Blum, J., 1955. On the convergence of empiric distributions. Ann. Math. Statist. 26, 527-529.
2. Budinger, T., et al., 1996. Mathematics and Physics of Emerging Biomedical Imaging. National Academic Press, Washington, DC.
3. Chiu, C.K., Glad, I.K., Godtliebsen, F., Marron, J.S., 1998. Edge-preserving smoothers for image processing. J. Amer. Statist. Assoc. 93, 526-556.
4. DeHardt, J., 1971. Generalizations of the Glivenko-Cantelli theorem. Ann. Math. Statist. 42, 2050-2055.
5. Godtliebsen, F., 1991. Noise reduction using Markov random fields. J. Magn. Reson. 92, 102-114.
6. Godtliebsen, F., Marron, S., 1997. A nonlinear Gaussian filter applied to images with discontinuities. J. Nonparametrics Statist. 8, 21-43.
7. Godtliebsen, F., Spjøtvoll, E., 1991. Comparison of statistical methods in MR imaging. Internat. J. Imag. Systems Tech. 3, 33-39.
8. Lee, J.S., 1983. Digital image smoothing and the sigma filter. Comput. Vision Graph. 24, 255-269.
9. Pawlak, M., Rafajłowicz, E., 2000. Vertically weighted regression - a tool for non-linear data analysis and constructing control charts. Amer. Statist. Assoc. 84, 367-388.
10. Pawlak, M., Rafajłowicz, E., 2001. Jump preserving signal reconstruction using vertical weighting. Nonlinear Anal - Theory 47, 327-338.
11. Pawlak, M., Rafajłowicz, E., Steland, A., 2004. Detecting jumps in time series - nonparametric setting. J. Nonparametrics Statist. 16, 329-347.
12. Shorack, G.R., Wellner, J.A., 1986. Empirical Processes with Applications to Statistics. Wiley, New York.
13. Steland, A., 2002a. Nonparametric monitoring of financial time series by jump-preserving estimators. Statist. Papers 43, 361-377.
14. Steland, A., 2004a. Jump-preserving monitoring of dependent time series under local alternatives. Statist. Decisions 21 (4), 343-366.
15. Steland, A., 2004b. Sequential control of time series by functionals of kernel-weighted empirical processes under local alternatives. Metrika, 60, 229-249.
16. Wolfram Research, 2004. Application documentation: digital image processing package. Section 5.5 〈http://documents.wolfram.com/applications/ digitalimage〉.