Segmentation spatiale et sélection de modèle : théorie et applications statistiques
Thèses d'Orsay, no. 638 (2003) , 304 p.
     author = {Chambaz, Antoine},
     title = {Segmentation spatiale et s\'election de mod\`ele : th\'eorie et applications statistiques},
     series = {Th\`eses d'Orsay},
     publisher = {Universit\'e Paris XI UFR scientifique d'Orsay},
     number = {638},
     year = {2003},
     language = {fr},
     url = {}
AU  - Chambaz, Antoine
TI  - Segmentation spatiale et sélection de modèle : théorie et applications statistiques
T3  - Thèses d'Orsay
PY  - 2003
IS  - 638
PB  - Université Paris XI UFR scientifique d'Orsay
UR  -
LA  - fr
ID  - BJHTUP11_2003__0638__A1_0
ER  - 
%0 Book
%A Chambaz, Antoine
%T Segmentation spatiale et sélection de modèle : théorie et applications statistiques
%S Thèses d'Orsay
%D 2003
%N 638
%I Université Paris XI UFR scientifique d'Orsay
%G fr
%F BJHTUP11_2003__0638__A1_0
Chambaz, Antoine. Segmentation spatiale et sélection de modèle : théorie et applications statistiques. Thèses d'Orsay, no. 638 (2003), 304 p.

Akaike, H. (1974). A new look at the statistical model identification. IEEE Trans. Automatic Control AC-19, 716-723. System identification and time-series analysis. | MR | Zbl | DOI

Antoniadis, A. and Berruyer, J. (1986). On estimating the number of components in a finite mixture of power series distributions. Comput. Statist. Data Anal. 4 (4), 229-241. | MR | Zbl | DOI

Antoniadis, A. and Gijbels, I. (2002). Detecting abrupt changes by wavelet methods. J. Non-parametr. Stat. 14 1-2), 7-29. | MR | Zbl | DOI

Antoniadis, A., Gijbels, I., and Macgibbon, B. (2000). Non-parametric estimation for the location of a change-point in an otherwise smooth hazard function under random censoring. Scand. J. Statist. 27 (3), 501-519. | MR | Zbl | DOI

Bahadur, R. R. (1967). An optimal property of the likelihood ratio statistic. In Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), Vol. I: Statistics, pp. 13-26. Berkeley, Calif.: Univ. California Press. | MR | Zbl

Bahadur, R. R. (1971). Some limit theorems in statistics. Philadelphia, Pa.: Society for Industrial and Applied Mathematics. Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 4. | MR | Zbl

Bahadur, R. R., Zabell, S. L., and Gupta, J. C. (1980). Large deviations, tests, and estimates. In Asymptotic theory of statistical tests and estimation (Proc. Adv. Internat. Sympos., Univ. North Carolina, Chapel Hill, N.C., 1979), pp. 33-64. New York: Academic Press. | MR | Zbl

Bai, Z. D., Rao, C. R., and Wu, Y. (1999). Model selection with data-oriented penalty. J. Statist. Plann. Inference 77(1), 103-117. | MR | Zbl | DOI

Barron, A., Birgé, L., and Massart, P. (1999). Risk bounds for model selection via penalization. Probab. Theory Related Fields 113(3), 301-413. | MR | Zbl | DOI

Basseville, M. and Nikiforov, I. V. (1993). Detection of abrupt changes: theory and application. Prentice Hall Inc. | MR | Zbl

Blanchard, G. (2001). Méthodes de mélange et d'agrégation d'estimateurs en reconnaissance de formes. Application aux arbres de décision. Ph. D. thesis, Université Paris XIII - Paris-Nord. Available at

Bousquet, O. and Elisseeff, A. (2002). Stability and generalization. Journal of Machine Learning Research 2, 499-526. | MR | Zbl

Breiman, L. (1996a). Bagging predictors. Machine Learning 24(2), 123-140. | Zbl | DOI

Breiman, L. (1996b). Heuristics of instability and stabilization in model selection. Ann. Statist. 24(6), 2350-2383. | MR | Zbl | DOI

Breiman, L. (1998). Arcing classifiers. Ann. Statist. 26(3), 801-849. With discussion and a rejoinder by the author. | MR | Zbl

Breiman, L. (2001). Statistical modeling: the two cultures. Statist. Sci. 16(3), 199-231. With comments and a rejoinder by the author. | MR | Zbl | DOI

Breiman, L., Friedman, J., Olshen, R., and Stone, C. (1984). Classification and regression trees. Chapman & Hall. | MR | Zbl

Brillinger (1990). Spatial-temporal modeling of spatially aggregate birth data. Survey Methodology Journal 16, 255-269.

Brodsky, B. E. and Darkhovsky, B. S. (1993). Nonparametric methods in change-point problems. Kluwer Academic Publishers Group. | MR | Zbl | DOI

Bühlmann, P. and Yu, B. (2002a). Analyzing bagging. Ann. Statist. 30(4), 927-961. | MR | Zbl | DOI

Bühlmann, P. and Yu, B. (2002b). Boosting with the L 2 -loss: regression and classification. Preprint. | MR | Zbl

Burkholder, D. L. (1973). Distribution function inequalities for martingales. Ann. Probability 1, 19-42. | MR | Zbl | DOI

Carlstein, E., Müller, H.-G., and Siegmund, D. (Eds.) (1994). Change-point problems. Hayward, CA: Institute of Mathematical Statistics. Papers from the AMS-IMS-SIAM Summer Research Conference held at Mt. Holyoke College, South Hadley, MA, July 11-16, 1992. | MR

Čencov, N. N. (1982). Statistical decision rules and optimal inference. Providence, R.I.: American Mathematical Society. Translation from the Russian edited by Lev J. Leifman. | MR | Zbl

Chambaz, A. (2002). Detecting abrupt changes in random fields. ESAIM P&S 6, 289-209. | MR | Numdam | DOI

Chernoff, H. (1956). Large sample theory: parametric case. Ann. Math. Statist. 27, 1-22. | MR | Zbl | DOI

Chou, P. A., Lookabaugh, T., and Gray, R. M. (1989). Optimal pruning with applications to tree-structured source coding and modeling. IEEE Trans. Inform. Theory 35(2), 299-315. | MR | DOI

Cressie, N. A. C. (1993). Statistics for spatial data. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. New York: John Wiley & Sons Inc. | MR | Zbl

Csiszár, I. (1975). I-divergence geometry of probability distributions and minimization problems. Ann. Probability 3, 146-158. | MR | Zbl | DOI

Dacunha-Castelle, D. and Gassiat, E. (1997). The estimation of the order of a mixture model. Bernoulli 3(3), 279-299. | MR | Zbl | DOI

Dacunha-Castelle, D. and Gassiat, E. (1999). Testing the order of a model using locally conic parametrization: population mixtures and stationary ARMA processes. Ann. Statist. 27(4), 1178-1209. | MR | Zbl | DOI

De Acosta, A. (1994). Projective systems in large deviation theory. II. Some applications. In Probability in Banach spaces, 9 (Sandjberg, 1993), pp. 241-250. Birkhäuser Boston. | MR | Zbl | DOI

Dedecker, J. (2001). Exponential inequalities and functional central limit theorem for random fields. ESAIM P&S 5. | MR | Zbl | Numdam | DOI

Dembo, A. and Zeitouni, O. (1998). Large deviations techniques and applications. New York: Springer-Verlag. | MR | Zbl | DOI

Donoho, D. L. (1997). CART and best-orthobasis: a connection. Ann. Statist. 25 (5), 1870-1911. | MR | Zbl | DOI

Doukhan, P. (1994). Mixing. New York: Springer-Verlag. Properties and examples. | MR | Zbl

Drucker, H. (1997). Improving regressors using boosting techniques. In Proc. 14th International Conference on Machine Learning, pp. 107-115. Morgan Kaufmann.

Dudley, R. M. and Philipp, W. (1983). Invariance principles for sums of Banach space valued random elements and empirical processes. Z. Wahrsch. Verw. Gebiete 62(4), 509-552. | MR | Zbl | DOI

Dupuis, P. and Ellis, R. S. (1997). A weak convergence approach to the theory of large deviations. Wiley Series in Probability and Statistics: Probability and Statistics. New York: John Wiley & Sons Inc. | MR | Zbl | DOI

Everitt, B. S. and Hand, D. J. (1981). Finite mixture distributions. London: Chapman & Hall. Monographs on Applied Probability and Statistics. | MR | Zbl

Feller, W. (1971). An introduction to probability theory and its applications. Vol. II. New York: John Wiley & Sons Inc. | MR | Zbl

Freund, Y. and Schapire, R. E. (1996). Experiments with a new boosting algorithm. In International Conference on Machine Learning, pp. 148-156.

Gassiat, E. (2002). Likelihood ratio inequalities with applications to various mixtures. To appear in Ann. Inst. H. Poincaré Probab. Statist. | MR | Zbl | Numdam | DOI

Gassiat, E. and Boucheron, S. (2001). Optimal error exponents in Hidden Markov Models order estimation. Preprint, submitted. | MR | Zbl

Gey, S. and Nedelec, E. (2001). Model selection for CART regression trees. Preprint. | MR | Zbl

Gey, S. and Poggi, J.-M. (2002). Boosting cart regression trees. Preprint.

Ghattas, B. (1999). Prévision par arbres de classification. Mathématiques, Informatique et Sciences Humaines 146, 31-50.

Ghosh, J. K. and Sen, P. K. (1985). On the asymptotic performance of the log likelihood ratio statistic for the mixture model and related results. In Proceedings of the Berkeley conference in honor of Jerzy Neyman and Jack Kiefer, Vol. II (Berkeley, Calif., 1983), Belmont, CA, pp. 789-806. Wadsworth. | MR | Zbl

Guyon, X. and Yao, J. (1999). On the underfitting and overfitting sets of models chosen by order selection criteria. J. Multivariate Anal. 70(2), 221-249. | MR | Zbl | DOI

Hastie, T., Tibshirani, R., and Friedman, J. (2001). The elements of statistical learning. New York: Springer-Verlag. Data mining, inference, and prediction. | MR | Zbl | DOI

Haughton, D. (1989). Size of the error in the choice of a model to fit data from an exponential family. Sankhyā Ser. A 51(1), 45-58. | MR | Zbl

Haughton, D. and Keribin, C. (2001). Asymptotic probabilities of overestimating and underestimating the order of a model in general regular families. Submitted. | MR | Zbl

Haughton, D. M. A. (1988). On the choice of a model to fit data from an exponential family. Ann. Statist. 16(1), 342-355. | MR | Zbl

Henna, J. (1985). On estimating of the number of constituents of a finite mixture of continuous distributions. Ann. Inst. Statist. Math. 37(2), 235-240. | MR | Zbl | DOI

Huber, P. J. (1967). The behavior of maximum likelihood estimates under nonstandard conditions. In Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), Vol. I: Statistics, pp. 221-233. Berkeley, Calif.: Univ. California Press. | MR | Zbl

James, L. F., Priebe, C. E., and Marchette, D. J. (2001). Consistent estimation of mixture complexity. Ann. Statist. 29 (5), 1281-1296. | MR | Zbl | DOI

Kallenberg, W. C. M. and Kourouklis, S. (1992). Hodges-Lehmann optimality of tests. Statist. Probab. Lett. 14(1), 31-38. | MR | Zbl | DOI

Keribin, C. (2000). Consistent estimation of the order of mixture models. Sankhyā Ser. A 62 (1), 49-66. | MR | Zbl

Korostelëv, A. P. and Tsybakov, A. B. (1993). Minimax theory of image reconstruction, Volume 82 of Lecture Notes in Statistics. New York: Springer-Verlag. | MR | Zbl

Kourouklis, S. (1991). Bahadur efficiency of likelihood ratio and related tests in nonregular models. Austral. J. Statist. 33 (3), 291-298. | MR | Zbl | DOI

Lagrange, X., Godlewski, P., and Tabbane, S. (1999). Réseaux GSM-DCS, des principes à la norme. Hermes Sciences Publications.

Lavielle, M.On the use of penalized contrasts for solving inverse problems. Application to the DDC (Detection of Divers Changes) problem. Submitted.

Lavielle, M. (1999). Detection of multiple changes in a sequence of dependent variables. Stochastic Process. Appl. 83(1), 79-102. | MR | Zbl | DOI

Lavielle, M. and Lebarbier, E. (2001). An application of MCMC methods for the multiple change-points problem. Signal Processing 81, 39-53. | Zbl | DOI

Lavielle, M. and Ludeña, C. (2000). The multiple change-points problem for the spectral distribution. Bernoulli 6(5), 845-869. | MR | Zbl | DOI

Lavielle, M. and Moulines, E. (2000). Least-squares estimation of an unknown number of shifts in a time series. J. Time Ser. Anal. 21 (1), 33-59. | MR | Zbl | DOI

Ledoux, M. (1992). Sur les déviations modérées des sommes de variables aléatoires vectorielles indépendantes de même loi. Ann. Inst. H. Poincaré Probab. Statist. 28(2), 267-280. | MR | Zbl | Numdam

Léonard, C. (2000). Minimizers of energy functionals under not very integrable constraints. Preprint. | Zbl

Léonard, C. and Najim, J. (2000). An extension of Sanov's theorem. Application to the Gibbs conditioning principle. Preprint. | MR | Zbl

Leonardi, G. P. and Tamanini, I. (2002). Metric spaces of partitions. Preprint. | MR | Zbl

Leroux, B. G. (1992). Consistent estimation of a mixing distribution. Ann. Statist. 20(3), 1350-1360. | MR | Zbl | DOI

Lindsay, B. G. (1989). Moment matrices: applications in mixtures. Ann. Statist. 17(2), 722-740. | MR | Zbl

Lindsay, B. G. and Lesperance, M. L. (1995). A review of semiparametric mixture models. J. Statist. Plann. Inference 47 (1-2), 29-39. Statistical modelling (Leuven, 1993). | MR | Zbl | DOI

Lugosi, G. (2000). Lectures on statistical learning theory. Presented at the Garchy Seminar on Mathematical Statistics and Applications, available at

Mallows (1973). Some comments on C p . Technometrics 15, 661-675. | Zbl

Mammen, E. and Tsybakov, A. B. (1995). Asymptotical minimax recovery of sets with smooth boundaries. Ann. Statist. 23 (2), 502-524. | MR | Zbl | DOI

Massart, P. (2000). Some applications of concentration inequalities to statistics. Ann. Fac. Sci. Toulouse Math. (6) 9(2), 245-303. | MR | Zbl | Numdam | DOI

Mclachlan, G. J. and Basford, K. E. (1988). Mixture models. New York: Marcel Dekker Inc. Inference and applications to clustering. | MR | Zbl

Móricz, F. (1983). A general moment inequality for the maximum of the rectangular partial sums of multiple series. Acta Math. Hungar. 41 (3-4), 337-346. | MR | Zbl | DOI

Móricz, F. A., Serfling, R. J., and Stout, W. F. (1982). Moment and probability bounds with quasisuperadditive structure for the maximum partial sum. Ann. Probab. 10(4), 1032-1040. | MR | Zbl | DOI

Müller, H.-G., Stadtmüller, U., and Tabnak, F. (1997). Spatial smoothing of geographically aggregated data, with application to the construction of incidence maps. J. Amer. Statist. Assoc. 92(437), 61-71. | MR | Zbl

Petrov, V. V. (1975). Sums of independent random variables. New York: Springer-Verlag. | MR | Zbl

Petrov, V. V. (1995). Limit theorems of probability theory. New York: The Clarendon Press Oxford University Press. Sequences of independent random variables, Oxford Science Publications. | MR | Zbl

Pollard, D. (1985). New ways to prove central limit theorems. Econometric Theory 1, 295-314. | DOI

Rao, M. M. and Ren, Z. D. (1991). Theory of Orlicz spaces. New York: Marcel Dekker Inc. | MR | Zbl

Rio, E. (2000). Théorie asymptotique des processus aléatoires faiblement dependants. Springer. | MR | Zbl

Rissanen, J. (1978). Modelling by shortest data description. Automatica 14, 465-471. | Zbl | DOI

Rockafellar, R. T. (1970). Convex analysis. Princeton University Press. | MR | Zbl | DOI

Schied, A. (1998). Cramer's condition and Sanov's theorem. Statist. Probab. Lett. 39, 55-60. | MR | Zbl | DOI

Schwarz, G. (1978). Estimating the dimension of a model. Ann. Statist. 6(2), 461-464. | MR | Zbl | DOI

Self, S. G. and Liang, K.-Y. (1987). Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. J. Amer. Statist. Assoc. 82(398), 605-610. | MR | Zbl | DOI

Senoussi, R. (1990). Statistique asymptotique presque sûre de modèles statistiques convexes. Ann. Inst. H. Poincaré Probab. Statist. 26 (1), 19-44. | MR | Zbl | Numdam

Serfling, R. J. (1968). Contributions to central limit theory for dependent variables. Ann. Math. Statist. 39, 1158-1175. | MR | Zbl | DOI

Talagrand, M. (1996a). New concentration inequalities in product spaces. Invent. Math. 126 (3), 505-563. | MR | Zbl | DOI

Talagrand, M. (1996b). A new look at independence. Ann. Probab. 24(1), 1-34. | MR | Zbl | DOI

Titterington, D. M., Smith, A. F. M., and Makov, U. E. (1985). Statistical analysis of finite mixture distributions. Chichester: John Wiley & Sons Ltd. | MR | Zbl

Van Der Vaart, A. W. (1998). Asymptotic statistics. Cambridge University Press. | MR | Zbl

Van Der Vaart, A. W. and Wellner, J. A. (1996). Weak convergence and empirical processes. New York: Springer-Verlag. With applications to statistics. | MR | Zbl | DOI

Vapnik, V. N. (1998). Statistical learning theory. New York: John Wiley & Sons Inc. | MR | Zbl

Wu, L. (1994). Large deviations, moderate deviations and LIL for empirical processes. Ann. Probab. 22(1), 17-27. | MR | Zbl

Yao, Y.-C. (1988). Estimating the number of change-points via Schwarz's criterion. Statist. Probab. Lett. 6(3), 181-189. | MR | Zbl | DOI

Ziemer, W. P. (1989). Weakly differentiable functions. New York: Springer-Verlag. Sobolev spaces and functions of bounded variation. | MR | Zbl