Estimation de la densité et tests par la méthode combinatoire pénalisée
Journal de la société française de statistique, Volume 144 (2003) no. 4, p. 5-24
@article{JSFS_2003__144_4_5_0,
     author = {Biau, G\'erard},
     title = {Estimation de la densit\'e et tests par la m\'ethode combinatoire p\'enalis\'ee},
     journal = {Journal de la soci\'et\'e fran\c caise de statistique},
     publisher = {Soci\'et\'e fran\c caise de statistique},
     volume = {144},
     number = {4},
     year = {2003},
     pages = {5-24},
     language = {fr},
     url = {http://www.numdam.org/item/JSFS_2003__144_4_5_0}
}
Biau, Gérard. Estimation de la densité et tests par la méthode combinatoire pénalisée. Journal de la société française de statistique, Volume 144 (2003) no. 4, pp. 5-24. http://www.numdam.org/item/JSFS_2003__144_4_5_0/

[1] Anthony M. et Bartlett P.L. (1999), Neural Network Learning : Theoretical Foundations, Cambridge University Press, Cambridge. | MR 1741038 | Zbl 0968.68126

[2] Barron A., Birgé L. et Massart P. (1999), Risk bounds for model selection via penalization, Probability Theory and Related Fields, Vol. 113, pp. 301-413. | MR 1679028 | Zbl 0946.62036

[3] Billingsley P. (1995), Probabihty and Measure, 3rd Edition, Wiley, New York. | MR 1324786 | Zbl 0649.60001

[4] Bishop C. L. (1994), Mixture density networks, Neural Computing Research Group Report NCRG/94/004, Department of Computer Science and Applied Mathematics, Aston University, Birmingham.

[5] Castellan G. (2000), Sélection d'histogrammes à l'aide d'un critère de type Akaike, Comptes Rendus de l'Académie des Sciences de Paris, Vol. 330, pp. 729-732. | MR 1763919 | Zbl 0969.62023

[6] Celeux G., Hurn M. et Robert C.P. (2000), Computational and inferential difficulties with mixture posterior distributions, Journal of the American Statistical Association, Vol. 95, pp. 957-970. | MR 1804450 | Zbl 0999.62020

[7] Dacunha-Castelle D. et Gassiat E. (1997), Testing in locally conic models, and application to mixture models, ESAIM : Probability and Statistics, Vol. 1, pp. 285-317. | Numdam | MR 1468112 | Zbl 1007.62507

[8] Dacunha-Castelle D. et Gassiat E. (1997), The estimation of the order of a mixture model, Bernoulh, Vol. 3, pp. 279-299. | MR 1468306 | Zbl 0889.62012

[9] Dacunha-Castelle D. et Gassiat E. (1999), Testing the order of a model using locally conic parametrization : population mixtures and stationary ARMA processes, The Annals of Statistics, Vol. 27, pp. 1178-1209. | MR 1740115 | Zbl 0957.62073

[10] Devroye L. (1997), A Course in Density Estimation, Birkhäuser, Boston. | MR 891874 | Zbl 0617.62043

[11] Devroye L. (1997). Universal smoothing factor selection in density estimation: theory and practice, Test, Vol. 6, pp. 223-320. | MR 1616896 | Zbl 0949.62026

[12] Devroye L., Gyorfi L. et Lugosi G. (2002), A note on robust hypothesis testing, IEEE Transactions on Information Theory, Vol. 48, pp. 2111-2114. | MR 1930019 | Zbl 1061.94513

[13] Devroye L. et Lugosi G. (2001), Combinatorial Methods in Density Estimation, Springer-Verlag, New York. | MR 1843146 | Zbl 0964.62025

[14] Diebolt J. et Robert C.P. (1994), Estimation of finite mixture distributions through Bayesian sampling, Journal of the Royal Statistical Society, Series B, Vol. 56, pp. 363-375. | MR 1281940 | Zbl 0796.62028

[15] Dudley R.M. (1978), Central limit theorems for empirical measures, The Annals of Probability, Vol. 6, pp. 899-929. | MR 512411 | Zbl 0404.60016

[16] Dunford N. et Schwartz J.T. (1963), Linear Operators Part I, Wiley, New York. | MR 1009162

[17] Everitt B.S. et Hand D.J. (1981), Finite Mixture Distributions, Chapman and Hall, London. | MR 624267 | Zbl 0466.62018

[18] Figueiredo M.A.T. et Jain A.K. (2002), Unsupervised learning of finite mixture models, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 24, pp. 381-396.

[19] Fukumizu K. (2003), Likelihood ratio of unidentifiable models and multilayer neural networks, The Annals of Statistics, Vol. 3 1 , pp. 833-851. | MR 1994732 | Zbl 1032.62020

[20] Hartigan J. (1985), A failure of likelihood asymptotics for normal mixtures, Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer, Volume II, pp. 807-810. | MR 822066

[21] Hurn M., Justel A. et Robert C.P. (2003), Estimating mixtures of regressions, Journal of Computational and Graphical Statistics, Vol. 12, pp. 1-25. | MR 1977206

[22] James L.F., Priebe C. E. et Marchette D.J. (2001), Consistent estimation of mixture complexity, The Annals of Statistics, Vol. 29, pp. 1281-1296. | MR 1873331 | Zbl 1043.62023

[23] Jordan M.I. et Jacobs R.A. (1994), Hierarchical mixtures of experts and the EM algorithm, Neural Computation, Vol. 6, pp. 181-214.

[24] Massart P. (2000), Some applications of concentration inequalities to statistics, Annales de la Faculté des Sciences de Toulouse, Vol. 9, pp. 245-303. | Numdam | MR 1813803 | Zbl 0986.62002

[25] Mcdiarmid C. (1989), On the method of bounded differences, in Surveys in Combinatorics 1989, pp. 148-188, Cambridge University Press, Cambridge. | MR 1036755 | Zbl 0712.05012

[26] Mclachlan G.J. (1987), On bootstrapping the likelihood ratio test statistic for the number of components in a normal mixture, Journal of Applied Statistics, Vol. 36, pp. 318-324.

[27] Mclachlan G.J. et Basford K.E. (1988), Mixture Models : Inference and Applications to Clustering, Marcel Dekker, New York. | MR 926484 | Zbl 0697.62050

[28] Mclachlan G.J. et Peel D. (2000), Finite Mixture Models, John Wiley, New York. | MR 1789474 | Zbl 0963.62061

[29] Priebe C. E. (1994), Adaptive mixtures, Journal of the American Statistical Association, Vol. 89, pp. 796-806. | MR 1294725 | Zbl 0825.62445

[30] Richardson S. et Green P.J. (1997), On Bayesian analysis of mixtures with an unknown number of components, Journal of the Royal Statistical Society, Series B, Vol. 59, pp. 731-792. | MR 1483213 | Zbl 0891.62020

[31] Roeder K. et Wasserman L. (1997), Practical Bayesian density estimation using mixtures of normals, Journal of the American Statistical Association, Vol. 92, pp. 894-902. | MR 1482121 | Zbl 0889.62021

[32] Rogers G.W., Marchette D.J. et Priebe C. E. (2002), A procedure for model complexity selection in semiparametric mixture model density estimation, Technical Report, Naval Surface Warfare Center, Dahlgren Division, Virginia.

[33] Titterington D.M., Smith A.F.M. et Makov U.E. (1985), Statistical Analysis of Finite Mixture Distributions, Wiley, Chichester. | MR 838090 | Zbl 0646.62013

[34] Vapnik V.N. et Chervonenkis A.Ya. (1971), On the uniform convergence of relative frequencies of events to their probabilities, Theory of Probabihty and its Applications, Vol. 16, pp. 264-280. | Zbl 0247.60005

[35] Yatracos Y.G. (1985), Rates of convergence of minimum distance estimators and Kolmogorov's entropy, The Annals of Statistics, Vol. 13, pp. 768-774. | MR 790571 | Zbl 0576.62057

[36] Zeevi A. et Meir R. (1997), Density estimation through convex combinations of densities ; approximation and estimation bounds, Neural Networks, Vol. 10, pp. 90-109. | Zbl 0869.68094