Detecting abrupt changes in random fields

Antoine Chambaz

ESAIM: Probability and Statistics (2010)

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

Abstract

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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

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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

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  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.  
  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.  
  3. Z.D. Bai, C.R. Rao and Y. Wu, Model selection with data-oriented penalty. J. Statist. Plann. Inference77 (1999) 103-117.  
  4. A. Barron, L. Birgé and P Massart, Risk bounds for model selection via penalization. Probab. Theory Related Fields113 (1999) 301-413.  
  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).  
  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.  
  9. J. Dedecker, Exponential inequalities and functional central limit theorems for random fields. ESAIM P&S5 (2001) 77.  
  10. P. Doukhan, Mixing. Springer-Verlag, New York (1994). Properties and examples.  
  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.  
  13. M. Lavielle and E. Lebarbier, An application of MCMC methods for the multiple change-points problem. Signal Process.81 (2001) 39-53.  
  14. M. Lavielle and C. Lude na, The multiple change-points problem for the spectral distribution. Bernoulli6 (2000) 845-869.  
  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.  
  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.  
  18. P. Massart, Some applications of concentration inequalities to statistics. Ann. Fac. Sci. Toulouse Math. (6)9 (2000) 245-303.  
  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.  
  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.  
  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.  
  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.  
  24. R.J. Serfling, Contributions to central limit theory for dependent variables. Ann. Math. Statist.39 (1968) 1158-1175.  
  25. M. Talagrand, New concentration inequalities in product spaces. Invent. Math.126 (1996) 505-563.  
  26. A.W. van der Vaart, Asymptotic statistics. Cambridge University Press (1998).  
  27. A.W. van der Vaart and J.A. Wellner, Weak convergence and empirical processes. Springer-Verlag, New York (1996). With applications to statistics.  
  28. V.N. Vapnik, Statistical learning theory. John Wiley & Sons Inc., New York (1998).  
  29. Y.-C. Yao, Estimating the number of change-points via Schwarz's criterion. Statist. Probab. Lett.6 (1988) 181-189.  

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