Rates of convergence for minimal distances in the central limit theorem under projective criteria

@inproceedings{Dedecker2007RatesOC,
  title={Rates of convergence for minimal distances in the central limit theorem under projective criteria},
  author={J{\'e}r{\^o}me Dedecker and Florence Merlev{\`e}de and E. Garc{\'i}a del R{\'i}o},
  year={2007}
}
Let X1, X2, . . . be a strictly stationary sequence of real-valued random variables (r.v.) with mean zero and finite variance. Set Sn = X1 +X2 + · · ·+Xn. By Pn−1/2Sn we denote the law of n−1/2Sn and by Gσ2 the normal distribution N(0, σ ). In this paper, we shall give quantitative estimates of the approximation of Pn−1/2Sn by Gσ2 in terms of minimal or ideal metrics. Let L(μ, ν) be the set of the probability laws on R with marginals μ and ν. Let us consider the following minimal distances… CONTINUE READING

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Showing 1-10 of 24 references

An empirical central limit theorem for dependent sequences

  • J. Dedecker, C. Prieur
  • Stoch. Processes
  • 2007
Highly Influential
13 Excerpts

Transformations dilatantes de l’intervalle et théorèmes limites

  • A. Broise
  • Études spectrales d’opérateurs de transfert et…
  • 1996
Highly Influential
11 Excerpts

Upper bounds for minimal distances in the central limit theorem

  • E. Rio
  • Submitted to Ann. Inst. H. Poincaré Probab…
  • 2007
Highly Influential
2 Excerpts

Théorie asymptotique des processus aléatoires faiblement dépendants

  • E. Rio
  • Mathématiques et applications de la SMAI. 31…
  • 2000
Highly Influential
2 Excerpts

Distances minimales et distances idéales

  • E. Rio
  • C. R. Acad. Sci. Paris Série I,
  • 1998
Highly Influential
2 Excerpts

Transformations dilatantes de l ’ intervalle et théorèmes limites . Études spectrales d ’ opérateurs de transfert et applications

  • A. Broise
  • 1996
Highly Influential
2 Excerpts

Approximating martingales and the central limit theorem for strictly stationary processes

  • D. Volný
  • Stoch. Processes Appl.,
  • 1993
Highly Influential
1 Excerpt

Estimates in an invariance principle

  • A. I. Sakhanenko
  • Trudy Inst. Mat.,
  • 1985
Highly Influential
2 Excerpts

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