Detecting abrupt changes in random fields

Antoine Chambaz

ESAIM: Probability and Statistics (2010)

  • Volume: 6, page 189-209
  • ISSN: 1292-8100

Abstract

top
This paper is devoted to the study of some asymptotic properties of a M-estimator in a framework of detection of abrupt changes in random field's distribution. This class of problems includes e.g. recovery of sets. It involves various techniques, including M-estimation method, concentration inequalities, maximal inequalities for dependent random variables and ϕ-mixing. Penalization of the criterion function when the size of the true model is unknown is performed. All the results apply under mild, discussed assumptions. Simple examples are provided.

How to cite

top

Chambaz, Antoine. "Detecting abrupt changes in random fields." ESAIM: Probability and Statistics 6 (2010): 189-209. <http://eudml.org/doc/104287>.

@article{Chambaz2010,
abstract = { This paper is devoted to the study of some asymptotic properties of a M-estimator in a framework of detection of abrupt changes in random field's distribution. This class of problems includes e.g. recovery of sets. It involves various techniques, including M-estimation method, concentration inequalities, maximal inequalities for dependent random variables and ϕ-mixing. Penalization of the criterion function when the size of the true model is unknown is performed. All the results apply under mild, discussed assumptions. Simple examples are provided. },
author = {Chambaz, Antoine},
journal = {ESAIM: Probability and Statistics},
keywords = {Detection of change-points; M-estimation; penalized M-estimation; concentration inequalities; maximal inequalities; mixing.},
language = {eng},
month = {3},
pages = {189-209},
publisher = {EDP Sciences},
title = {Detecting abrupt changes in random fields},
url = {http://eudml.org/doc/104287},
volume = {6},
year = {2010},
}

TY - JOUR
AU - Chambaz, Antoine
TI - Detecting abrupt changes in random fields
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 6
SP - 189
EP - 209
AB - This paper is devoted to the study of some asymptotic properties of a M-estimator in a framework of detection of abrupt changes in random field's distribution. This class of problems includes e.g. recovery of sets. It involves various techniques, including M-estimation method, concentration inequalities, maximal inequalities for dependent random variables and ϕ-mixing. Penalization of the criterion function when the size of the true model is unknown is performed. All the results apply under mild, discussed assumptions. Simple examples are provided.
LA - eng
KW - Detection of change-points; M-estimation; penalized M-estimation; concentration inequalities; maximal inequalities; mixing.
UR - http://eudml.org/doc/104287
ER -

References

top
  1. H. Akaike, A new look at the statistical model identification. IEEE Trans. Automat. ControlAC-19 (1974) 716-723. System identification and time-series analysis.  Zbl0314.62039
  2. A. Antoniadis, I. Gijbels and B. MacGibbon, Non-parametric estimation for the location of a change-point in an otherwise smooth hazard function under random censoring. Scand. J. Statist.27 (2000) 501-519.  Zbl0977.62034
  3. Z.D. Bai, C.R. Rao and Y. Wu, Model selection with data-oriented penalty. J. Statist. Plann. Inference77 (1999) 103-117.  Zbl0926.62045
  4. A. Barron, L. Birgé and P Massart, Risk bounds for model selection via penalization. Probab. Theory Related Fields113 (1999) 301-413.  Zbl0946.62036
  5. M. Basseville and I.V. Nikiforov, Detection of abrupt changes: Theory and application. Prentice Hall Inc. (1993).  
  6. B.E. Brodsky and B.S. Darkhovsky, Nonparametric methods in change-point problems. Kluwer Academic Publishers Group (1993).  Zbl1274.62512
  7. E. Carlstein, H.-G. Müller and D. Siegmund, Change-point problems. Institute of Mathematical Statistics, Hayward, CA (1994). Papers from the AMS-IMS-SIAM Summer Research Conference held at Mt. Holyoke College, South Hadley, MA July 11-16, 1992.  
  8. D. Dacunha-Castelle and E. Gassiat, The estimation of the order of a mixture model. Bernoulli3 (1997) 279-299.  Zbl0889.62012
  9. J. Dedecker, Exponential inequalities and functional central limit theorems for random fields. ESAIM P&S5 (2001) 77.  Zbl1003.60033
  10. P. Doukhan, Mixing. Springer-Verlag, New York (1994). Properties and examples.  Zbl0801.60027
  11. M. Lavielle, On the use of penalized contrasts for solving inverse problems. Application to the DDC (Detection of Divers Changes) problem (submitted).  
  12. M. Lavielle, Detection of multiple changes in a sequence of dependent variables. Stochastic Process. Appl.83 (1999) 79-102.  Zbl0991.62014
  13. M. Lavielle and E. Lebarbier, An application of MCMC methods for the multiple change-points problem. Signal Process.81 (2001) 39-53.  Zbl1098.94557
  14. M. Lavielle and C. Lude na, The multiple change-points problem for the spectral distribution. Bernoulli6 (2000) 845-869.  Zbl0998.62077
  15. M. Lavielle and E. Moulines, Least-squares estimation of an unknown number of shifts in a time series. J. Time Ser. Anal.21 (2000) 33-59.  Zbl0974.62070
  16. G. Lugosi, Lectures on statistical learning theory. Presented at the Garchy Seminar on Mathematical Statistics and Applications, available at http://www.econ.upf.es/~lugosi (2000).  
  17. E. Mammen and A.B. Tsybakov, Asymptotical minimax recovery of sets with smooth boundaries. Ann. Statist.23 (1995) 502-524.  Zbl0834.62038
  18. P. Massart, Some applications of concentration inequalities to statistics. Ann. Fac. Sci. Toulouse Math. (6)9 (2000) 245-303.  Zbl0986.62002
  19. F. Móricz, A general moment inequality for the maximum of the rectangular partial sums of multiple series. Acta Math. Hungar.41 (1983) 337-346.  Zbl0521.60017
  20. F.A. Móricz, R.J. Serfling and W.F. Stout, Moment and probability bounds with quasisuperadditive structure for the maximum partial sum. Ann. Probab.10 (1982) 1032-1040.  Zbl0499.60052
  21. V.V. Petrov, Limit theorems of probability theory. The Clarendon Press Oxford University Press, New York (1995). Sequences of independent random variables, Oxford Science Publications.  Zbl0826.60001
  22. E. Rio, Théorie asymptotique des processus aléatoires faiblement dépendants. Springer (2000).  
  23. G. Schwarz, Estimating the dimension of a model. Ann. Statist.6 (1978) 461-464.  Zbl0379.62005
  24. R.J. Serfling, Contributions to central limit theory for dependent variables. Ann. Math. Statist.39 (1968) 1158-1175.  Zbl0176.48004
  25. M. Talagrand, New concentration inequalities in product spaces. Invent. Math.126 (1996) 505-563.  Zbl0893.60001
  26. A.W. van der Vaart, Asymptotic statistics. Cambridge University Press (1998).  Zbl0910.62001
  27. A.W. van der Vaart and J.A. Wellner, Weak convergence and empirical processes. Springer-Verlag, New York (1996). With applications to statistics.  Zbl0862.60002
  28. V.N. Vapnik, Statistical learning theory. John Wiley & Sons Inc., New York (1998).  Zbl0935.62007
  29. Y.-C. Yao, Estimating the number of change-points via Schwarz's criterion. Statist. Probab. Lett.6 (1988) 181-189.  Zbl0642.62016

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.