@article{PS_1997__1__35_0, author = {Rio, Emmanuel}, title = {About the {Lindeberg} method for strongly mixing sequences}, journal = {ESAIM: Probability and Statistics}, pages = {35--61}, publisher = {EDP-Sciences}, volume = {1}, year = {1997}, mrnumber = {1382517}, zbl = {0869.60021}, 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, Tome 1 (1997), pp. 35-61. http://www.numdam.org/item/PS_1997__1__35_0/
Sur la compatibilité des fonctions de répartition. C.R. Acad. Sci. Paris. 240 839-841. | MR | Zbl
, ( 1955),On the convergence of sums of random variables in distribution under mixing condition. Periodica math. Hungarica. 2 173-190 | MR | Zbl
, ( 1972),Approximation theorems for independent and weakly dependent random vectors. Ann. Probab. 7 29-54. | MR | Zbl
and ( 1979),The Berry-Esseen theorem for functionals of discrete Markov chains. Z. Wahrsch. verw. Gebiete. 54 59-73. | MR | Zbl
, ( 1980),The Berry-Esseen theorem for strongly mixing Harris recurrent Markov chains. Z. Wahrsch. verw. Gebiete 60 283-289. | MR | Zbl
, ( 1982),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 | Zbl
and , ( 1990),Convergence of distributions generated by stationary stochastic processes. Theory Probab. Appl. 13 691-696. | Zbl
, ( 1968),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.
, ( 1991),Mixing. Properties and Examples. Lecture Notes in Statistics 85. Springer, New York. | MR | Zbl
, ( 1994),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 | Zbl
, and , ( 1984),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 | Zbl
, and , ( 1985),The functional central limit Theorem for strongly mixing processes. Annales inst. H. Poincaré Probab. Statist. 30 63-82. | Numdam | MR | Zbl
, and , ( 1994),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
and , ( 1983a),Moments de variables aléatoires mélangeantes, C. R. Acad. Sci. Paris, Série 1, 297 129-132. | MR | Zbl
and , ( 1983b),Principe d'invariance faible pour la fonction de répartition empirique dans un cadre multidimensionnel et mélangeant. Probab. Math. Stat. 8 117-132. | MR | Zbl
and , ( 1987),Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law. Acta Math. 77 1-125. | MR | Zbl
, ( 1945),Sur les tableaux de corrélation dont les marges sont données. Annales de l'université de Lyon, Sciences, section A. 14 53-77. | MR | Zbl
, ( 1951),Sur la distance de deux lois de probabilité. C. R. Acad. Sci. Paris 244 689-692. | MR | Zbl
, ( 1957),The central limit theorem for stationary processes. Soviet Math. Dokl. 10 1174-1176. | MR | Zbl
, ( 1969),Asymptotic expansions for sums of weakly dependent random vectors. Z. Wahrsch. verw. Gebiete. 64 211-239. | MR | Zbl
and , ( 1983),Martingale limit theory and its applications, Academic Press. | MR | Zbl
and , ( 1980),Some limit theorems for stationary processes. 7 349-382. | MR | Zbl
, ( 1962),Independent and stationary sequences of random variables, Wolters-Noordhoff, Amsterdam. | MR | Zbl
and , ( 1971),A new look at Bergström's theorem on convergence in distribution for sums of dependent random variables. Israel J. Math. 47 32-64. | MR | Zbl
, ( 1984),Eine neue Herleitung des Exponentialgezetzes in der Wahrscheinlichkeitsrechnung. Mathematische Zeitschrift, 15 211-225. | JFM | MR
, ( 1922),On the asymptotic normality of sequences of weak dependent random variables. To appear in J. of Theoret. Probab. | MR | Zbl
, ( 1995),Central limit theorem for stationary linear processes. Preprint. | MR
and , ( 1994),Sums of independent random variables. Springer, Berlin. | MR | Zbl
, ( 1975),Covariance inequalities for strongly mixing processes. Annales inst. H. Poincaré Probab. Statist. 29 587-597. | Numdam | MR | Zbl
, ( 1993),Inégalités de moments pour les suites stationnaires et fortement mélangeantes. C. R. Acad. Sci. Paris, Série I. 318 355-360. | MR | Zbl
, ( 1994),A central limit theorem and a strong mixing condition. Proc. Natl. Acad. Sci. U.S.A. 42 43-47. | MR | Zbl
, ( 1956),On the subspaces of Lp, (p > 2) spanned by sequences of independent random variables. Israel J. Math. 8 273-303. | MR | Zbl
, ( 1970),Convergence of sums of mixing triangular arrays of random vectors with stationary rows. Ann. Probab. 12 390-426. | MR | Zbl
, ( 1984),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 | Zbl
, ( 1972),On the convergence rate in the central limit theorem for weakly dependent random variables. Theor. Probab. Appl. 25 790-809. | MR | Zbl
, ( 1980),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
, ( 1985),Moment bounds for stationary mixing sequences. Z. Wahrsch. verw. Gebiete. 52 45-57. | MR | Zbl
, ( 1980),On the error of the Gaussian approximation for convolutions. Theory Probab. Appl. 22 236-247. | MR | Zbl
, ( 1977),