About the Lindeberg method for strongly mixing sequences
ESAIM: Probability and Statistics, Volume 1  (1997), p. 35-61
@article{PS_1997__1__35_0,
     author = {Rio, Emmanuel},
     title = {About the Lindeberg method for strongly mixing sequences},
     journal = {ESAIM: Probability and Statistics},
     publisher = {EDP-Sciences},
     volume = {1},
     year = {1997},
     pages = {35-61},
     zbl = {0869.60021},
     mrnumber = {1382517},
     language = {en},
     url = {http://www.numdam.org/item/PS_1997__1__35_0}
}
Rio, Emmanuel. About the Lindeberg method for strongly mixing sequences. ESAIM: Probability and Statistics, Volume 1 (1997) , pp. 35-61. http://www.numdam.org/item/PS_1997__1__35_0/

Bass, J., ( 1955), Sur la compatibilité des fonctions de répartition. C.R. Acad. Sci. Paris. 240 839-841. | MR 68149 | Zbl 0064.12804

Bergström, H., ( 1972), On the convergence of sums of random variables in distribution under mixing condition. Periodica math. Hungarica. 2 173-190 | MR 350814 | Zbl 0252.60009

Berkes, I. and Philipp, W. ( 1979), Approximation theorems for independent and weakly dependent random vectors. Ann. Probab. 7 29-54. | MR 515811 | Zbl 0392.60024

Bolthausen, E., ( 1980), The Berry-Esseen theorem for functionals of discrete Markov chains. Z. Wahrsch. verw. Gebiete. 54 59-73. | MR 595481 | Zbl 0431.60019

Bolthausen, E., ( 1982), The Berry-Esseen theorem for strongly mixing Harris recurrent Markov chains. Z. Wahrsch. verw. Gebiete 60 283-289. | MR 664418 | Zbl 0476.60022

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. | MR 1082637 | Zbl 0719.60020

Davydov, Yu. A., ( 1968), Convergence of distributions generated by stationary stochastic processes. Theory Probab. Appl. 13 691-696. | Zbl 0181.44101

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. | MR 1312160 | Zbl 0801.60027

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. | MR 765429 | Zbl 0557.60006

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. | MR 845525 | Zbl 0607.60019

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. | Numdam | MR 1262892 | Zbl 0790.60037

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. | Zbl 0529.60029

Doukhan, P. and Portal, F., ( 1983b), Moments de variables aléatoires mélangeantes, C. R. Acad. Sci. Paris, Série 1, 297 129-132. | MR 720925 | Zbl 0544.62022

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. | MR 928125 | Zbl 0651.60042

Esseen, C., ( 1945), Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law. Acta Math. 77 1-125. | MR 14626 | Zbl 0060.28705

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. | MR 49518 | Zbl 0045.22905

Fréchet, M., ( 1957), Sur la distance de deux lois de probabilité. C. R. Acad. Sci. Paris 244 689-692. | MR 83210 | Zbl 0077.33007

Gordin, M. I., ( 1969), The central limit theorem for stationary processes. Soviet Math. Dokl. 10 1174-1176. | MR 251785 | Zbl 0212.50005

Gótze, F. and Hlpp, C., ( 1983), Asymptotic expansions for sums of weakly dependent random vectors. Z. Wahrsch. verw. Gebiete. 64 211-239. | MR 714144 | Zbl 0497.60022

Hall, P. and Heyde, C. C., ( 1980), Martingale limit theory and its applications, Academic Press. | MR 624435 | Zbl 0462.60045

Ibragimov, I. A., ( 1962), Some limit theorems for stationary processes. 7 349-382. | MR 148125 | Zbl 0119.14204

Ibragimov, I. A. and Linnik, Y. V., ( 1971), Independent and stationary sequences of random variables, Wolters-Noordhoff, Amsterdam. | MR 322926 | Zbl 0219.60027

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. | MR 736063 | Zbl 0536.60032

Llndeberg, J. W., ( 1922), Eine neue Herleitung des Exponentialgezetzes in der Wahrscheinlichkeitsrechnung. Mathematische Zeitschrift, 15 211-225. | JFM 48.0602.04 | MR 1544569

Peligrad, M., ( 1995), On the asymptotic normality of sequences of weak dependent random variables. To appear in J. of Theoret. Probab. | MR 1400595 | Zbl 0855.60021

Peligrad, M. and Utev, S., ( 1994), Central limit theorem for stationary linear processes. Preprint. | MR 2257658

Petrov, V. V., ( 1975), Sums of independent random variables. Springer, Berlin. | MR 388499 | Zbl 0322.60042

Rio, E., ( 1993), Covariance inequalities for strongly mixing processes. Annales inst. H. Poincaré Probab. Statist. 29 587-597. | Numdam | MR 1251142 | Zbl 0798.60027

Rio, E., ( 1994), Inégalités de moments pour les suites stationnaires et fortement mélangeantes. C. R. Acad. Sci. Paris, Série I. 318 355-360. | MR 1267615 | Zbl 0797.60011

Rosenblatt, M., ( 1956), A central limit theorem and a strong mixing condition. Proc. Natl. Acad. Sci. U.S.A. 42 43-47. | MR 74711 | Zbl 0070.13804

Rosenthal, H. P., ( 1970), On the subspaces of Lp, (p > 2) spanned by sequences of independent random variables. Israel J. Math. 8 273-303. | MR 271721 | Zbl 0213.19303

Samur, J. D., ( 1984), Convergence of sums of mixing triangular arrays of random vectors with stationary rows. Ann. Probab. 12 390-426. | MR 735845 | Zbl 0542.60012

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. | MR 402873 | Zbl 0278.60026

Tlkhomirov, A. N., ( 1980), On the convergence rate in the central limit theorem for weakly dependent random variables. Theor. Probab. Appl. 25 790-809. | MR 595140 | Zbl 0471.60030

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. | Zbl 0591.60016

Yokoyama, R., ( 1980), Moment bounds for stationary mixing sequences. Z. Wahrsch. verw. Gebiete. 52 45-57. | MR 568258 | Zbl 0407.60002

Yurinskii, V. V., ( 1977), On the error of the Gaussian approximation for convolutions. Theory Probab. Appl. 22 236-247. | MR 517490 | Zbl 0378.60008