Geodesic
Rates of Convergence in the CLT for Some Weakly Dependent Random Variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 2, pp. 345-364

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We provide rates in the central limit theorem (CLT) for some weakly dependent sequences under a power decay of their covariance. Those sequences are assumed to be associated with or to satisfy a common property of Gaussian processes and positively (or negatively) dependent random variables. For this, we extend the Lindeberg method in our framework, following a method due to [E. Rio, Probab. Theory Related Fields, 104 (1996), pp. 255–282] The method of the proofs also provides upper bounds of the Dudley distances between the distribution of a normalized sum of those weak dependent random variables and the standard normal distribution. It also leads to Rosenthal-type inequalities for moments of partial sums. for mixing sequences.
Keywords: positive dependence, negative dependence, Berry–Esseen theorem, Lindeberg central limit theorem, moment inequalities, Rosenthal's inequalities.
Mots-clés : association 
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     author = {S. Louhichi},
     title = {Rates of {Convergence} in the {CLT} for {Some} {Weakly} {Dependent} {Random} {Variables}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {345--364},
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     volume = {46},
     number = {2},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2001_46_2_a7/}
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S. Louhichi. Rates of Convergence in the CLT for Some Weakly Dependent Random Variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 2, pp. 345-364. http://geodesic.mathdoc.fr/item/TVP_2001_46_2_a7/