Estimation de la densité et tests par la méthode combinatoire pénalisée

Gérard Biau

Journal de la société française de statistique (2003)

  • Volume: 144, Issue: 4, page 5-24
  • ISSN: 1962-5197

How to cite


Biau, Gérard. "Estimation de la densité et tests par la méthode combinatoire pénalisée." Journal de la société française de statistique 144.4 (2003): 5-24. <>.

author = {Biau, Gérard},
journal = {Journal de la société française de statistique},
language = {fre},
number = {4},
pages = {5-24},
publisher = {Société française de statistique},
title = {Estimation de la densité et tests par la méthode combinatoire pénalisée},
url = {},
volume = {144},
year = {2003},

AU - Biau, Gérard
TI - Estimation de la densité et tests par la méthode combinatoire pénalisée
JO - Journal de la société française de statistique
PY - 2003
PB - Société française de statistique
VL - 144
IS - 4
SP - 5
EP - 24
LA - fre
UR -
ER -


  1. [1] ANTHONY M. et BARTLETT P.L. (1999), Neural Network Learning : Theoretical Foundations, Cambridge University Press, Cambridge. Zbl0968.68126MR1741038
  2. [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. Zbl0946.62036MR1679028
  3. [3] BILLINGSLEY P. (1995), Probabihty and Measure, 3rd Edition, Wiley, New York. Zbl0649.60001MR1324786
  4. [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. [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. Zbl0969.62023MR1763919
  6. [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. Zbl0999.62020MR1804450
  7. [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. Zbl1007.62507MR1468112
  8. [8] DACUNHA-CASTELLE D. et GASSIAT E. (1997), The estimation of the order of a mixture model, Bernoulh, Vol. 3, pp. 279-299. Zbl0889.62012MR1468306
  9. [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. Zbl0957.62073MR1740115
  10. [10] DEVROYE L. (1997), A Course in Density Estimation, Birkhäuser, Boston. Zbl0617.62043MR891874
  11. [11] DEVROYE L. (1997). Universal smoothing factor selection in density estimation: theory and practice, Test, Vol. 6, pp. 223-320. Zbl0949.62026MR1616896
  12. [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. Zbl1061.94513MR1930019
  13. [13] DEVROYE L. et LUGOSI G. (2001), Combinatorial Methods in Density Estimation, Springer-Verlag, New York. Zbl0964.62025MR1843146
  14. [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. Zbl0796.62028MR1281940
  15. [15] DUDLEY R.M. (1978), Central limit theorems for empirical measures, The Annals of Probability, Vol. 6, pp. 899-929. Zbl0404.60016MR512411
  16. [16] DUNFORD N. et SCHWARTZ J.T. (1963), Linear Operators Part I, Wiley, New York. MR1009162
  17. [17] EVERITT B.S. et HAND D.J. (1981), Finite Mixture Distributions, Chapman and Hall, London. Zbl0466.62018MR624267
  18. [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. [19] FUKUMIZU K. (2003), Likelihood ratio of unidentifiable models and multilayer neural networks, The Annals of Statistics, Vol. 3 1 , pp. 833-851. Zbl1032.62020MR1994732
  20. [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. MR822066
  21. [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. MR1977206
  22. [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. Zbl1043.62023MR1873331
  23. [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. [24] MASSART P. (2000), Some applications of concentration inequalities to statistics, Annales de la Faculté des Sciences de Toulouse, Vol. 9, pp. 245-303. Zbl0986.62002MR1813803
  25. [25] McDIARMID C. (1989), On the method of bounded differences, in Surveys in Combinatorics 1989, pp. 148-188, Cambridge University Press, Cambridge. Zbl0712.05012MR1036755
  26. [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. [27] McLACHLAN G.J. et BASFORD K.E. (1988), Mixture Models : Inference and Applications to Clustering, Marcel Dekker, New York. Zbl0697.62050MR926484
  28. [28] McLACHLAN G.J. et PEEL D. (2000), Finite Mixture Models, John Wiley, New York. Zbl0963.62061MR1789474
  29. [29] PRIEBE C. E. (1994), Adaptive mixtures, Journal of the American Statistical Association, Vol. 89, pp. 796-806. Zbl0825.62445MR1294725
  30. [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. Zbl0891.62020MR1483213
  31. [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. Zbl0889.62021MR1482121
  32. [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. [33] TITTERINGTON D.M., SMITH A.F.M. et MAKOV U.E. (1985), Statistical Analysis of Finite Mixture Distributions, Wiley, Chichester. Zbl0646.62013MR838090
  34. [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. Zbl0247.60005
  35. [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. Zbl0576.62057MR790571
  36. [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. Zbl0869.68094

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