About the Lindeberg method for strongly mixing sequences
ESAIM: Probability and Statistics (1997)
- Volume: 1, page 35-61
- ISSN: 1292-8100
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topRio, Emmanuel. "About the Lindeberg method for strongly mixing sequences." ESAIM: Probability and Statistics 1 (1997): 35-61. <http://eudml.org/doc/104240>.
@article{Rio1997,
author = {Rio, Emmanuel},
journal = {ESAIM: Probability and Statistics},
keywords = {deviation inequalities; concentration of measure; logarithmic Sobolev inequalities; empirical processes; central limit theorem; strongly mixing triangular arrays; Lévy distance},
language = {eng},
pages = {35-61},
publisher = {EDP Sciences},
title = {About the Lindeberg method for strongly mixing sequences},
url = {http://eudml.org/doc/104240},
volume = {1},
year = {1997},
}
TY - JOUR
AU - Rio, Emmanuel
TI - About the Lindeberg method for strongly mixing sequences
JO - ESAIM: Probability and Statistics
PY - 1997
PB - EDP Sciences
VL - 1
SP - 35
EP - 61
LA - eng
KW - deviation inequalities; concentration of measure; logarithmic Sobolev inequalities; empirical processes; central limit theorem; strongly mixing triangular arrays; Lévy distance
UR - http://eudml.org/doc/104240
ER -
References
top- BASS, J., ( 1955), Sur la compatibilité des fonctions de répartition. C.R. Acad. Sci. Paris. 240 839-841. Zbl0064.12804MR68149
- BERGSTRÖM, H., ( 1972), On the convergence of sums of random variables in distribution under mixing condition. Periodica math. Hungarica. 2 173-190 Zbl0252.60009MR350814
- BERKES, I. and PHILIPP, W. ( 1979), Approximation theorems for independent and weakly dependent random vectors. Ann. Probab. 7 29-54. Zbl0392.60024MR515811
- BOLTHAUSEN, E., ( 1980), The Berry-Esseen theorem for functionals of discrete Markov chains. Z. Wahrsch. verw. Gebiete. 54 59-73. Zbl0431.60019MR595481
- BOLTHAUSEN, E., ( 1982), The Berry-Esseen theorem for strongly mixing Harris recurrent Markov chains. Z. Wahrsch. verw. Gebiete 60 283-289. Zbl0476.60022MR664418
- BULINSKII, A. V. and DOUKHAN, P., ( 1990), Vitesse de convergence dans le théorème de limite centrale pour des champs mélangeants satisfaisant des hypothèses de moment faibles. C. R. Acad. Sci. Paris, Série 1, 311 801-805. Zbl0719.60020MR1082637
- DAVYDOV, YU. A., ( 1968), Convergence of distributions generated by stationary stochastic processes. Theory Probab. Appl. 13 691-696. Zbl0181.44101
- DOUKHAN, P., ( 1991), Consistency of δ-estimates for a regression or a density in a dependent framework. Séminaire d'Orsay 1989-1990: Estimation fonctionnelle. Prépublication mathématique de l'université de Paris-Sud.
- DOUKHAN, P., ( 1994), Mixing. Properties and Examples. Lecture Notes in Statistics 85. Springer, New York. Zbl0801.60027MR1312160
- DOUKHAN, P., LÉON, J. and PORTAL, F., ( 1984), Vitesse de convergence dans le théorème central limite pour des variables aléatoires mélangeantes à valeurs dans un espace de Hilbert. C. R. Acad. Sci. Paris Série 1, 298 305-308. Zbl0557.60006MR765429
- DOUKHAN, P., LÉON, J. and PORTAL, F., ( 1985), Calcul de la vitesse de convergence dans le théorème central limite vis à vis des distances de Prohorov, Dudley et Lévy dans le cas de variables aléatoires dépendantes. Probab. Math. Stat. 6 19-27. Zbl0607.60019MR845525
- DOUKHAN, P., MASSART, P. and Rio, E., ( 1994), The functional central limit Theorem for strongly mixing processes. Annales inst. H. Poincaré Probab. Statist. 30 63-82. Zbl0790.60037MR1262892
- DOUKHAN, P. and PORTAL, F., ( 1983a), Principe d'invariance faible avec vitesse pour un processus empirique dans un cadre multidimensionnel et fortement mélangeant. C. R. Acad. Sci. Paris, Série 1, 297 505-508. Zbl0529.60029
- DOUKHAN, P. and PORTAL, F., ( 1983b), Moments de variables aléatoires mélangeantes, C. R. Acad. Sci. Paris, Série 1, 297 129-132. Zbl0544.62022MR720925
- DOUKHAN, P. and PORTAL, F., ( 1987), Principe d'invariance faible pour la fonction de répartition empirique dans un cadre multidimensionnel et mélangeant. Probab. Math. Stat. 8 117-132. Zbl0651.60042MR928125
- ESSEEN, C., ( 1945), Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law. Acta Math. 77 1-125. Zbl0060.28705MR14626
- FRÉCHET, M., ( 1951), Sur les tableaux de corrélation dont les marges sont données. Annales de l'université de Lyon, Sciences, section A. 14 53-77. Zbl0045.22905MR49518
- FRÉCHET, M., ( 1957), Sur la distance de deux lois de probabilité. C. R. Acad. Sci. Paris 244 689-692. Zbl0077.33007MR83210
- GORDIN, M. I., ( 1969), The central limit theorem for stationary processes. Soviet Math. Dokl. 10 1174-1176. Zbl0212.50005MR251785
- GÓTZE, F. and HlPP, C., ( 1983), Asymptotic expansions for sums of weakly dependent random vectors. Z. Wahrsch. verw. Gebiete. 64 211-239. Zbl0497.60022MR714144
- HALL, P. and Heyde, C. C., ( 1980), Martingale limit theory and its applications, Academic Press. Zbl0462.60045MR624435
- IBRAGIMOV, I. A., ( 1962), Some limit theorems for stationary processes. 7 349-382. Zbl0119.14204MR148125
- IBRAGIMOV, I. A. and LINNIK, Y. V., ( 1971), Independent and stationary sequences of random variables, Wolters-Noordhoff, Amsterdam. Zbl0219.60027MR322926
- KRIEGER, H. A., ( 1984), A new look at Bergström's theorem on convergence in distribution for sums of dependent random variables. Israel J. Math. 47 32-64. Zbl0536.60032MR736063
- LlNDEBERG, J. W., ( 1922), Eine neue Herleitung des Exponentialgezetzes in der Wahrscheinlichkeitsrechnung. Mathematische Zeitschrift, 15 211-225. MR1544569JFM48.0602.04
- PELIGRAD, M., ( 1995), On the asymptotic normality of sequences of weak dependent random variables. To appear in J. of Theoret. Probab. Zbl0855.60021MR1400595
- PELIGRAD, M. and UTEV, S., ( 1994), Central limit theorem for stationary linear processes. Preprint. MR2257658
- PETROV, V. V., ( 1975), Sums of independent random variables. Springer, Berlin. Zbl0322.60042MR388499
- RIO, E., ( 1993), Covariance inequalities for strongly mixing processes. Annales inst. H. Poincaré Probab. Statist. 29 587-597. Zbl0798.60027MR1251142
- RIO, E., ( 1994), Inégalités de moments pour les suites stationnaires et fortement mélangeantes. C. R. Acad. Sci. Paris, Série I. 318 355-360. Zbl0797.60011MR1267615
- ROSENBLATT, M., ( 1956), A central limit theorem and a strong mixing condition. Proc. Natl. Acad. Sci. U.S.A. 42 43-47. Zbl0070.13804MR74711
- ROSENTHAL, H. P., ( 1970), On the subspaces of Lp, (p > 2) spanned by sequences of independent random variables. Israel J. Math. 8 273-303. Zbl0213.19303MR271721
- SAMUR, J. D., ( 1984), Convergence of sums of mixing triangular arrays of random vectors with stationary rows. Ann. Probab. 12 390-426. Zbl0542.60012MR735845
- STEIN, C., ( 1972), A bound on the error in the normal approximation to the distribution of a sum of dependent random variables. Proc. Sixth Berkeley Symp. Math. Statist. and Prob. II 583-602. Zbl0278.60026MR402873
- TlKHOMIROV, A. N., ( 1980), On the convergence rate in the central limit theorem for weakly dependent random variables. Theor. Probab. Appl. 25 790-809. Zbl0471.60030MR595140
- UTEV, S., ( 1985), Inequalities and estimates of the convergence rate for the weakly dependent case. Proceedings of the institut e of mathematics Novosibirsk. Limit theorems for sums of random variables. Adv. in Probab. Theory. 73-114. Editor A. A. Borovkov. Optimization Software, Inc. New York. Zbl0591.60016
- YOKOYAMA, R., ( 1980), Moment bounds for stationary mixing sequences. Z. Wahrsch. verw. Gebiete. 52 45-57. Zbl0407.60002MR568258
- YURINSKII, V. V., ( 1977), On the error of the Gaussian approximation for convolutions. Theory Probab. Appl. 22 236-247. Zbl0378.60008MR517490
Citations in EuDML Documents
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- Clémentine Prieur, Density estimation for one-dimensional dynamical systems
- Clémentine Prieur, Density Estimation for One-Dimensional Dynamical Systems
- Jérôme Dedecker, Emmanuel Rio, On mean central limit theorems for stationary sequences
- Paul Doukhan, José R. León, Asymptotics for the -deviation of the variance estimator under diffusion
- Michael H. Neumann, A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics
- Paul Doukhan, José R. León, Asymptotics for the -deviation of the variance estimator under diffusion
- Nadine Guillotin-Plantard, Clémentine Prieur, Central limit theorem for sampled sums of dependent random variables
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