Performances d'un test d'homogénéité contre une hypothèse de mélange gaussien

A. Berdaï; B. Garel

Revue de Statistique Appliquée (1994)

  • Volume: 42, Issue: 1, page 63-79
  • ISSN: 0035-175X

How to cite


Berdaï, A., and Garel, B.. "Performances d'un test d'homogénéité contre une hypothèse de mélange gaussien." Revue de Statistique Appliquée 42.1 (1994): 63-79. <>.

author = {Berdaï, A., Garel, B.},
journal = {Revue de Statistique Appliquée},
language = {fre},
number = {1},
pages = {63-79},
publisher = {Société de Statistique de France},
title = {Performances d'un test d'homogénéité contre une hypothèse de mélange gaussien},
url = {},
volume = {42},
year = {1994},

AU - Berdaï, A.
AU - Garel, B.
TI - Performances d'un test d'homogénéité contre une hypothèse de mélange gaussien
JO - Revue de Statistique Appliquée
PY - 1994
PB - Société de Statistique de France
VL - 42
IS - 1
SP - 63
EP - 79
LA - fre
UR -
ER -


  1. Andrews D.F., Bickel P.J., Hampel F.R., Huber P.J., Rogers W.M., Tukey J.W. (1972), Robust Estimates of Location. Princeton University Press. Zbl0254.62001MR331595
  2. Berdaï A. (1991), Une étude asymptotique et numérique de la loi limite du test de mélange de deux lois contre une seule. Technical report, S.B.I.A., I.N.R.A.Toulouse. 
  3. Cramer H., Leadbetter M.R. (1967), Stationnary and related stochastic Process. New York: Wiley. Zbl0162.21102MR217860
  4. Davies R.B. (1977), Hypothesis testing when a nuisance parameter is present only under the atemative. Biometrika,64, 247- 254. Zbl0362.62026MR501523
  5. Davies R.B. (1987), Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika,74, 33- 43. Zbl0612.62023MR885917
  6. Ghosh J.K., Sen P.K. (1985), On the asymptotic performance of the Log likelihood ratio statistic for the mixture model and related results. Proc. Berkeley Conference in honor of Jerzy Neyman and Jack Kiefer (vol.II), L.M. Le Cam and R.A. Olshen (Eds.). Monterey: Wadsworth, p. 789-806. MR822065
  7. Hartigan J.A.(1985a), Statistical theory in clustering. J.Classification, 2, 63-76. Zbl0575.62058MR800514
  8. Hartigan J.A.(1985b), A failure of likelihood asymptotics for normal mixtures, Proc. Berkeley Conference in honor of Jerzy Neymann and Jack Kiefer (vol.99), L. M. Le Cam and R.A. Oshen (Eds). Monterey Zbl0575.62045
  9. Kotz S., Johnson N.L. (1983), Encyclopedia of Statistical Sciences, vol.4, p. 3-4. Zbl0585.62002
  10. McLachlan G.J., Basford K.E. (1988), Mixture models : Inference and applications to clustering. Marcel Dekker, New York. Zbl0697.62050MR926484
  11. Mendell N.R., Thode H.C., Finch S.J., (1991), The likelihood ratio test for two component normal mixture problem : power and sample size analysis. Biometrics, 47, 1143 -1148. 
  12. Redner R.A.(1981), Note on the consistency of the maximum likelihood estimate for non identifiable distributions. Ann. Statist., 9, 225- 228. Zbl0453.62021MR600553
  13. Self S.G., Liang K.Y. (1987), Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under non standard conditions. JASA, vol. 82, N° 398, 605-610. Zbl0639.62020MR898365
  14. Thode H.C., Finch S.J., Mendel N.R. (1988), Simulated percentage points for the null distribution of the likelihood ratio test for a mixture of two normals. Biometrics, 44, 1195-1201. Zbl0715.62040MR981003
  15. Titterington D.M. (1990), Some recent research in the analysis of mixture distributions. Statistics, 21,4, 619-641. Zbl0714.62023MR1087291
  16. Titterington D.M., Smith A.F.M., Makov U.E. (1985), Statistical analysis of finite mixture distributions. Wiley, London. Zbl0646.62013MR838090
  17. Yakowitz S.J., Spragins J.D. (1968), On the identifiability of finite mixtures. IEEE Trans. Inform. Th., IT-16, 330- 338. Zbl0197.45502
  18. Wald A. (1943), Tests of statistical hypotheses concerning several parameters when the number of observations is large. Trans. Am. Math. Soc, 54, 426 -482. Zbl0063.08120MR12401
  19. Wolfe J.H. (1971), A Monte Carlo study of the sampling distribution of the likelihhod ratio for mixtures of multinomial distributions. Tech. Bull. STB,72-2, Nav. Pers & Tran. Res. Lab., San Diego. 

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