Asymptotic normality in mixture models

Sara Van De Geer

ESAIM: Probability and Statistics (1997)

  • Volume: 1, page 17-33
  • ISSN: 1292-8100

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Van De Geer, Sara. "Asymptotic normality in mixture models." ESAIM: Probability and Statistics 1 (1997): 17-33. <http://eudml.org/doc/104230>.

@article{VanDeGeer1997,
author = {Van De Geer, Sara},
journal = {ESAIM: Probability and Statistics},
keywords = {Asymptotic efficiency; asymptotic normality; differentiable functionals; linear integral functional; mixture model; nonparametric maximum likelihood estimator; NPMLE},
language = {eng},
pages = {17-33},
publisher = {EDP Sciences},
title = {Asymptotic normality in mixture models},
url = {http://eudml.org/doc/104230},
volume = {1},
year = {1997},
}

TY - JOUR
AU - Van De Geer, Sara
TI - Asymptotic normality in mixture models
JO - ESAIM: Probability and Statistics
PY - 1997
PB - EDP Sciences
VL - 1
SP - 17
EP - 33
LA - eng
KW - Asymptotic efficiency; asymptotic normality; differentiable functionals; linear integral functional; mixture model; nonparametric maximum likelihood estimator; NPMLE
UR - http://eudml.org/doc/104230
ER -

References

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  1. BIRGÉ, L. and MASSART, P., ( 1993), Rates of convergence for minimum contrast estimators, Probab. Th. Relat. Fields 97 113-150. Zbl0805.62037MR1240719
  2. BIRMAN, M. and SOLOMJAK, M.J., ( 1967), Piece-wise polynomial approximations of functions of the classes W∞p, Mat. Sbornik 73 295-317. Zbl0173.16001
  3. GROENEBOOM, P. and WELLNER, J.A., ( 1992), Information Bounds and Nonparametric Maximum Likelihood Estimation, BMW Seminar, Band 19, Birkhäuser. Zbl0757.62017MR1180321
  4. OSSIANDER, M. ( 1987), A central limit theorem under metric entropy with L2 bracketing, Ann. Probab. 15 897-919. Zbl0665.60036MR893905
  5. PFANZAGL, J., ( 1988), Consistency of maximum likelihood estimators for certain nonparametric families, in particular: mixtures, J. Statist. Plann. Inference 19 137-158. Zbl0656.62044MR944202
  6. POLLARD, D. ( 1984), Convergence of Stochastic Processes, Springer, New York. Zbl0544.60045MR762984
  7. VAN DE GEER, S. ( 1990), Estimating a regression function, Ann. Statist. 18 907-924. Zbl0709.62040MR1056343
  8. VAN DE GEER, S., ( 1991), The entropy bound for monotone functions, Techn. Report TW 91-10, Univ. of Leiden. 
  9. VAN DE GEER, S. ( 1993a), Hellinger consistency of certain nonparametric maximum likelihood estimators, Ann. Statist. 21 14-44. Zbl0779.62033MR1212164
  10. VAN DE GEER, S. ( 1993b), Rates of convergence for the maximum likelihood estimator in mixture models, Techn. Report TW 93-09, Univ. of Leiden. 
  11. VAN DE GEER, S. ( 1995), The method of sieves and minimum contrast estimators, Mathematical Methods of Statistics 4 20-38. Zbl0831.62029MR1324688
  12. VAN DER LAAN, M.J. ( 1993), Efficient and Inefficient Estimation in Semiparametric Models Thesis, Univ. of Utrecht. To appear as CWI tract 44, Centre for Math. and Comp. Sci., Amsterdam. Zbl0838.62003MR1376813
  13. VAN DER LAAN, M. J. ( 1994), Proving efficiency of NPMLE and identities, Techn. Report 44, Un. of California, Berkeley. 
  14. VAN DER VAART, A.W. ( 1991), On differentiable functionals, Ann. Statist. 19 178-205. Zbl0732.62035MR1091845
  15. WONG, W.H. and SHEN, X. ( 1992), Probability inequalities for likelihood ratios and convergence rates for sieve MLE's, Techn. Report 346, Univ. of Chicago. 

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