Metadata
Abstract
In this paper, we give estimates of the quadratic transportation cost in the conditional central limit theorem for a large class of dependent sequences. Applications to irreducible Markov chains, dynamical systems generated by intermittent maps and -mixing sequences are given.
References
[Bil61] The Lindeberg–Lévy theorem for martingales, Proc. Am. Math. Soc., Volume 12 (1961), pp. 788-792 | Zbl
[Bob13] Entropic approach to E. Rio’s central limit theorem for transport distance, Stat. Probab. Lett., Volume 83 (2013) no. 7, pp. 1644-1648 | DOI | MR | Zbl
[Bob18] Berry–Esseen bounds and Edgeworth expansions in the central limit theorem for transport distances, Probab. Theory Relat. Fields, Volume 170 (2018) no. 1, pp. 1-2 | MR | Zbl
[Bol82] The Berry–Esseen theorem for strongly mixing Harris recurrent Markov chains, Z. Wahrscheinlichkeitstheor. Verw. Geb., Volume 60 (1982), pp. 283-289 | DOI | MR | Zbl
[Bon20] Stein’s method for normal approximation in Wasserstein distances with application to the multivariate central limit theorem, Probab. Theory Relat. Fields, Volume 178 (2020) no. 3-4, pp. 827-860 | DOI | MR | Zbl
[DGM10] Some almost sure results for unbounded functions of intermittent maps and their associated Markov chains, Ann. Inst. Henri Poincaré, Probab. Stat., Volume 46 (2010) no. 3, pp. 796-821 | Numdam | MR | Zbl
[DL01] The central limit theorem for Markov chains with normal transition operators, started at a point, Probab. Theory Relat. Fields, Volume 119 (2001) no. 4, pp. 508-528 | DOI | MR | Zbl
[DM15] Moment bounds for dependent sequences in smooth Banach spaces, Stochastic Processes Appl., Volume 125 (2015) no. 9, pp. 3401-3429 | DOI | MR | Zbl
[DMR09] Rates of convergence for minimal distances in the central limit theorem under projective criteria, Electron. J. Probab., Volume 14 (2009) no. 35, pp. 978-1011 | MR | Zbl
[DP05] New dependence coefficients. Examples and applications to statistics, Probab. Theory Relat. Fields, Volume 132 (2005) no. 2, pp. 203-236 | DOI | MR | Zbl
[DR08] On mean central limit theorems for stationary sequence, Ann. Inst. Henri Poincaré, Probab. Stat., Volume 44 (2008) no. 4, pp. 693-726 | MR | Zbl
[Fan19] Wasserstein-2 bounds in normal approximation under local dependence, Electron. J. Probab., Volume 24 (2019), 35 | MR | Zbl
[Ibr63] A central limit theorem for a class of dependent random variables, Theory Probab. Appl., Volume 8 (1963), pp. 89-94 | MR | Zbl
[JWZ21] Sharp connections between Berry–Esseen characteristics and Edgeworth expansions for stationary processes, Trans. Am. Math. Soc., Volume 374 (2021) no. 6, pp. 4129-4183 | DOI | MR | Zbl
[Kom55] Elementary inequalities for Mills’ ratio, Rep. Statist. Appl. Res. Un. Japan. Sci. Engrs., Volume 4 (1955), pp. 69-70 | MR
[LSV99] A probabilistic approach to intermittency, Ergodic Theory Dyn. Syst., Volume 19 (1999) no. 3, pp. 671-685 | DOI | MR | Zbl
[MPU19] Functional Gaussian Approximation for Dependent Structures, Oxford Studies in Probability, 6, Oxford University Press, 2019 | DOI | Zbl
[MR12] Strong approximation of partial sums under dependence conditions with application to dynamical systems, Stochastic Processes Appl., Volume 122 (2012) no. 1, pp. 386-417 | MR | Zbl
[Pin14] An optimal three-way stable and monotonic spectrum of bounds on quantiles: a spectrum of coherent measures of financial risk and economic inequality, Risks, Volume 2 (2014) no. 3, pp. 349-392 | DOI
[Pèn05] Rate of convergence in the multidimensional central limit theorem for stationary processes. Application to the Knudsen gas and to the Sinai billiard, Ann. Appl. Probab., Volume 15 (2005) no. 4, pp. 2331-2392 | MR | Zbl
[Rio09] Upper bounds for minimal distances in the central limit theorem, Ann. Inst. Henri Poincaré, Probab. Stat., Volume 45 (2009) no. 3, pp. 802-817 | Numdam | MR | Zbl
[Rio17a] About the conditional value at risk of partial sums, C. R. Math. Acad. Sci. Paris, Volume 355 (2017) no. 11, pp. 1190-1195 | Numdam | MR | Zbl
[Rio17b] Asymptotic theory of weakly dependent random processes, Probability Theory and Stochastic Modelling, 80, Springer, 2017 | Zbl
[Sch80] Diophantine approximation, Lecture Notes in Mathematics, 785, Springer, 1980 | Zbl
[Vil09] Optimal transport. Old and new, Grundlehren der Mathematischen Wissenschaften, 338, Springer, 2009 | DOI | Zbl