Almost sure invariance principle for the Kantorovich distance between the empirical and the marginal distributions of strong mixing sequences

DOI10.1016/j.spl.2020.108991zbMath1457.60051OpenAlexW3101917834MaRDI QIDQ2657995

Jérôme Dedecker, Florence Merlevède

Publication date: 18 March 2021

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spl.2020.108991

zbMATH Keywords

empirical processWasserstein distanceconditional value at riskalmost sure invariance principlecompact law of the iterated logarithmbounded law of the iterated logarithm

Mathematics Subject Classification ID

Stationary stochastic processes (60G10) Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (2)

Central limit theorem and almost sure results for the empirical estimator of superquantiles/CVaR in the stationary case ⋮ The Berry–Esseen-type bound for the G-M estimator in a nonparametric regression model with α-mixing errors

Cites Work

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• Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary \(\alpha\)-dependent sequences
• About the conditional value at risk of partial sums
• Central limit theorems for the Wasserstein distance between the empirical and the true distributions
• Optimum bounds for the distributions of martingales in Banach spaces
• Asymptotic theory of weakly dependent stochastic processes
• Invariance principles under the Maxwell-Woodroofe condition in Banach spaces
• A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION

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