Testing in locally conic models, and application to mixture models
ESAIM: Probability and Statistics, Volume 1  (1997), p. 285-317
@article{PS_1997__1__285_0,
author = {Dacunha-Castelle, Didier and Gassiat, \'E.},
title = {Testing in locally conic models, and application to mixture models},
journal = {ESAIM: Probability and Statistics},
publisher = {EDP-Sciences},
volume = {1},
year = {1997},
pages = {285-317},
zbl = {1007.62507},
mrnumber = {1468112},
language = {en},
url = {http://www.numdam.org/item/PS_1997__1__285_0}
}

Dacunha-Castelle, D.; Gassiat, É. Testing in locally conic models, and application to mixture models. ESAIM: Probability and Statistics, Volume 1 (1997) , pp. 285-317. http://www.numdam.org/item/PS_1997__1__285_0/

Adler, R. J. ( 1990). An introduction to continuity, extrema, and related topics for general Gaussian processes. IMS Lecture Notes-Monograph Series. | MR 1088478 | Zbl 0747.60039

Azais, J. M. and Wschebor, M. ( 1995). A formula to compute the distribution of the maximum of a random process. Université P. Sabatier, Toulouse.

Azencott, R. and Dacunha-Castelle, D. ( 1984). Séries d'observations irrégulières. Masson. | MR 746133 | Zbl 0546.62060

Beran, R. and Millar, P. W. ( 1987). Stochastic estimation and testing. Annals of Stat., 15 1131-1154. | MR 902250 | Zbl 0644.62028

Berdai, A. and Garel, B. ( 1994). Performances d'un test d'homogénéité contre une hypothèse de mélange gaussien. Rev. Stat. Appl. 42 63-79. | Numdam | MR 1278467 | Zbl 0972.62505

Bickel, P. and Chernoff, H. ( 1993). Asymptotic distribution of the likelihood ratio statistic in a prototypical non regular problem. In Statistics and Probability: A Raghu Raj Bahadur Festschrift.

Dacunha-Castelle, D. and Duflo, M. ( 1986). Probability and Statistics. Springer Verlag New-York. | Zbl 0586.62003

Dacunha-Castelle, D. and Gassiat, E. ( 1996). Testing the order of a model using locally conic parametrization: population mixtures and stationary ARMA processes. Submitted. | Zbl 0957.62073

Donoho, D. L. ( 1988). One-sided inference about functionals of a density. Annals of Stat. 16 1390-1420. | MR 964930 | Zbl 0665.62040

Dudley, R. M. ( 1967). The size of compact subsets of hilbert space and continuity of Gaussian processes. Journal of Funct. Analysis 1 290-330. | MR 220340 | Zbl 0188.20502

Ghosh, J. and Sen, P. ( 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. Le Cam, L.M. and Olshen, R.A. eds. | MR 822065

Hannan, E. J. ( 1982). Testing for autocorrelation and akaike's criterion. In Essays in Statistical Science, p. 403-412. Gani, J.M., Hannan, E.J. eds. | MR 633209 | Zbl 0498.62078

Hartigan, J. A. ( 1985). A failure of likelihood ratio asymptotics for normal mixtures. In Proceedings of the Berkeley conference in honor of Jerzy Neyman and Jack Kiefer. Le Cam, L.M. and Olshen, R.A. eds.

Laurent, B. ( 1993). Estimation de fonctionnelles intégrales non linéaires de la densité et de ses dérivées. PhD thesis, Université de Paris XI, France.

Ossiander, M. ( 1987). A central limit theorem under metric entropy with l2 bracketing. Annals of Prob. 15 897-919. | MR 893905 | Zbl 0665.60036

Redner, R. ( 1981). Note on the consistency of the maximum likelihood estimate for nonidentifiable distributions. Annals of Stat. 9 225-228. | MR 600553 | Zbl 0453.62021

Roussas, G. G. ( 1970). Contiguity of probability measures: some applications in statistics. Princeton University press. | MR 359099 | Zbl 1152.60007

Self, S. and Liang, K. ( 1987). Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. Jour. Amer. Stat. Assoc. 823 605-610. | MR 898365 | Zbl 0639.62020

Teicher, H. ( 1965). Identifiability of finite mixtures. Annals of Math. Statist. 36 423-439. | MR 155376

Van Der Vaart, A. W. and Wellner, J. A. ( 1996). Empirical Processes. Springer Verlag.

Yakowitz, S. J. and Spragins, J. D. ( 1968). On the identifiability of finite mixtures. Annals of Math. Stat. 39 209-214. | MR 224204 | Zbl 0155.25703