Quelques exemples de problèmes inverses en statistique et en traitement du signal
Revue de Statistique Appliquée, Volume 45 (1997) no. 4, p. 5-38
@article{RSA_1997__45_4_5_0,
     author = {Lavielle, M. and Moulines, \'Eric},
     title = {Quelques exemples de probl\`emes inverses en statistique et en traitement du signal},
     journal = {Revue de Statistique Appliqu\'ee},
     publisher = {Soci\'et\'e de Statistique de France},
     volume = {45},
     number = {4},
     year = {1997},
     pages = {5-38},
     language = {fr},
     url = {http://www.numdam.org/item/RSA_1997__45_4_5_0}
}
Lavielle, M.; Moulines, E. Quelques exemples de problèmes inverses en statistique et en traitement du signal. Revue de Statistique Appliquée, Volume 45 (1997) no. 4, pp. 5-38. http://www.numdam.org/item/RSA_1997__45_4_5_0/

[1] Basseville M. and Nikiforov N. (1993), The Detection of abrupt changes - Theory and applications, Prentice-Hall: Information and System sciences series. | MR 1210954

[2] Benveniste A., Metivier M., and Priouret P. (1987), Algorithmes adaptatifs et approximations stochastiques, Masson. | Zbl 0639.93002

[3] Besag J.E. (1986), «On the statistical analysis of dirty pictures», J. R. Statist. Soc. B, vol. 48, pp. 259- 302. | MR 876840 | Zbl 0609.62150

[4] Binder D.A. (1978), «Bayesian clustering analysis», Biometrika, vol. 68, pp.275-286. | MR 501592 | Zbl 0376.62007

[5] Biscarat J.C. (1994), «Almost sure convergence of a class of stochastic approximation algorithms», Stoch. Proc. Appl., vol. 50, pp. 83-100. | MR 1262332 | Zbl 0819.60033

[6] Blake A. and Zisserman A. (1987), Visual Reconstruction. Cambridge, MA: MIT Press. | MR 919733

[7] Brandiere O. and Duflo M. (1996), «Les algorithmes stochastiques contournent-ils les pièges ?», Annales de l'Institut H. Poincaré, vol. 32, pp. 395-427. | Numdam | MR 1387397 | Zbl 0849.62043

[8] Brodsky B.E. and Darkhovsky B.S. (1993), Nonparametric methods in change-point problems. Kluwer Academic Publishers, the Netherlands. | MR 1228205 | Zbl 0779.62031

[9] Cardoso J.F. and Moulines E. (1994), «How much more DOA information in higher-order statistics?», in Proc. Int. Conf. on Acoust. Speech and Sig. Proc, pp. 199- 202.

[10] Catoni O. (1992), «Rough large deviation estimates for simulated annealing : application to exponential shedules», The Annals of Proba., vol. 20, no. 3, pp. 1109- 1146. | MR 1175253 | Zbl 0755.60021

[11] Celeux G. and Diebolt J. (1985), «The SEM algorithm : a probabilistic teacher algorithm derived from the EM algorithm for the mixture problem», Computational Statistics Quarterly, vol. 2, pp. 73- 82.

[12] Celeux G. and Diebolt J. (1992), «A stochastic approximation type EM algorithm for the mixture problem», Stoch. and Stoch. Reports, vol. 41, pp. 119-134. | MR 1275369 | Zbl 0766.62050

[13] Delyon B. (1996), « General results on stochastic approximation », IEEE Trans. On Autom. Control, 41, pp. 1245-1255. | MR 1409470 | Zbl 0867.93075

[ 14] Dempster A., Laird N., and Rubin D. (1977), « Maximum-likelihood from incomplete data via the EM algorithm», J. R. Statist. Soc. B, vol. 39, pp. 1- 38. | MR 501537 | Zbl 0364.62022

[15] Deshayes J. and Picard D. (1986), «Off-line statistical analysis of change point models using non-parametric and likelihood method », in Detection of abrupt changes in signals and systems, Lecture Notes in Control and Information Sciences, pp. 259-275, Edited by M. Basseville et A. Benveniste.

[16] Donoho D. (1981), « On minimum entropy deconvolution », in Applied time-series analysis II, pp. 565 -609, Academic Press. | Zbl 0481.62075

[17] Duflo M. (1996), Algorithmes Stochastiques. SMAI, Springer. | MR 1612815 | Zbl 0882.60001

[18] Gamboa F. and Gassiat E. (1996), «Blind deconvolution of discrete linear systems», The Annals of Stat., vol. 24, 1964-1981. | MR 1421156 | Zbl 0867.62073

[19] Fort J.C. and Pagès G. (1996), «Convergence of stochastic algorithms : from Kushner-Clark theorem to the Lyapounov functional method », Adv .appl. prob., vol. 28, pp. 1072-1094. | MR 1418247 | Zbl 0881.62085

[20] Gaeta M. and Lacoume J.L. (1990), «Estimateurs du maximum de vraisemblance étendus à la séparation de sources non gaussiennes», Traitement du Signal, vol. 7, no. 5, pp. 419-434. | MR 1097385

[21] Gelfand A.E. and Smith A.F.M. (1990), «Sampling based approach for calculating marginal densities», J. Amer. Stat. Assoc., vol. 85, pp. 398-409. | MR 1141740 | Zbl 0702.62020

[22] Gelfand S.B. and Mitter S.K. (1993), «Metropolis-type annealing algorithms for global optimization in IRd*», SIAM J. Control and optimization, vol. 31, no. 1, pp. 111-131. | MR 1200226 | Zbl 0814.65059

[23] Geman D. (1990), Random Fields and Inverse Problems in Imaging. Lecture Notes in Mathematics, Springer-Verlag. | MR 1100283 | Zbl 0718.60119

[24] Geman S. and Geman D. (1984), «Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images», IEEE Trans. on Pattern Anal. Machine Intell., vol. 6, pp. 721-741. | Zbl 0573.62030

[25] Hawkins D.M. (1980), «Identification of outliers », in Monographs on Applied Probability and Statistics, Chapman and Hall. | MR 584791 | Zbl 0438.62022

[26] Jutten C. and Hérault J. (1988), «Une solution neuromimétique au problème de séparation de sources», Traitement du Signal, vol. 5, no. 6, pp. 389-403.

[27] Kaufman L. and Rousseuw P.J. (1990), Finding groups in data. An introduction to cluster analysis. Wiley: New-York. | MR 1044997

[28] Kirkpatrick S., Gelatt C.D., and Vecchi M.P. (1983), «Optimisation by simulated annealing», Science, vol. 220, no. 13 May, pp. 621-680. | MR 702485 | Zbl 1225.90162

[29] Lavielle M. (1991), «2-D Bayesian deconvolution », Geophysics, vol. 56, no. 12, pp. 2008-2018.

[30] Lavielle M. (1993), «Bayesian deconvolution of Bernoulli-Gaussian processes», Signal Processing, vol. 33, pp. 67-79. | Zbl 0788.62024

[3 1 ] Lavielle M. (1993), «Detection of changes in the spectrum of a multidimensional process», IEEE Tr. on Sig. Proc., vol. 41, no. 2, pp. 742-749. | Zbl 0825.93760

[32] Lavielle M. (1995), «A stochastic procedure for parametric and nonparametric estimation in the case of incomplete data », Signal Processing, vol. 42, pp.3-17. | Zbl 0871.62084

[33] Lavielle M. and Moulines E. (1995), «On a stochastic approximation version of the EM algorithm», tech. rep., Publication Université Paris-Sud.

[34] Lavielle M. and Moulines E. (1997), «Détection de ruptures multiples dans la moyenne d'un processus aléatoire», note C.R. Acad. Sci. Paris, t. 324, I, pp. 239-243. | MR 1438392 | Zbl 0882.60031

[35] Picard D. (1985), «Testing and estimating change points in time series», J. Applied Prob., vol. 17, pp. 841-867. | MR 809433 | Zbl 0585.62151

[36] Qian W. and Titterington D.M. (1991), «Estimation of parameters in hidden Markov models», Phil. Trans. Roy. Soc. London, A, vol. 337, pp. 407-428. | Zbl 0746.62086

[37] Robert C.P. (1996), Méthodes de Monte Carlo par Chaînes de Markov. Statistique mathématique et Probabilité, Economica. | MR 1419096 | Zbl 0917.60007

[38] Rosenfeld A. and Kak A. (1982), Digital picture processing, vol. 2. London: Academic-Press. | MR 666550 | Zbl 0564.94002

[39] Shalvi O. and Weinstein E. (1990), « New criteria for blind deconvolution of nonminimum phase systems (channels », IEEE Tr. on Info. Theory, vol. 36, no. 2, pp. 312- 321. | Zbl 0704.94001

[40] Titterington D.M., Smith A., and Makov U. (1985), Statistical analysis of finite mixture distributions. Wiley- New York. | MR 838090 | Zbl 0646.62013

[41] Wei G. and Tanner M. (1990), «A Monte-Carlo implementation of the EM algorithm and the Poor's Man's data augmentation algorithm», J. Amer Stat. Assoc., vol. 85, pp. 699-704.

[42] Wu C. (1983), «On the convergence property of the EM algorithm », The Annals of Stat., vol. 11, pp. 95-103. | MR 684867

[43] Younes L. (1989), «Parametric inference for imperfectly observed Gibbsian fields», Prob. Theory Rel. Fields, vol. 82, pp. 625-645. | MR 1002904 | Zbl 0659.62115