An empirical central limit theorem in L\(^1\) for stationary sequences

DOI10.1016/j.spa.2009.06.006zbMath1176.60022arXiv0812.2839OpenAlexW2007503182MaRDI QIDQ734650

Sophie Dede

Publication date: 13 October 2009

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.2839

zbMATH Keywords

central limit theoremempirical distribution functionWasserstein distanceergodic stationary sequence

Mathematics Subject Classification ID

Order statistics; empirical distribution functions (62G30) Stationary stochastic processes (60G10) Functional limit theorems; invariance principles (60F17)

Related Items (5)

Distribution of Distances based Object Matching: Asymptotic Inference ⋮ Statistical Inference for Expectile‐based Risk Measures ⋮ Empirical optimal transport on countable metric spaces: distributional limits and statistical applications ⋮ On the weak invariance principle for ortho-martingale in Banach spaces. Application to stationary random fields ⋮ Donsker results for the empirical process indexed by functions of locally bounded variation and applications to the smoothed empirical process

Cites Work

• Unnamed Item
• Unnamed Item
• Probability in Banach spaces. Isoperimetry and processes
• Covariance inequalities
• Central limit theorem for stationary linear processes
• Approximating martingales and the central limit theorem for strictly stationary processes
• Central limit theorem and stable laws for intermittent maps
• New dependence coefficients. Examples and applications to statistics
• Central limit theorems for the Wasserstein distance between the empirical and the true distributions
• Asymptotic theory of weakly dependent stochastic processes
• On the weak invariance principle for non-adapted sequences under projective criteria
• A new covariance inequality and applications.
• A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION
• A probabilistic approach to intermittency
• The Lindeberg-Levy Theorem for Martingales
• The empirical distribution function for dependent variables: asymptotic and nonasymptotic results in ${\mathbb L}^p$
• Some Limit Theorems for Stationary Processes
• Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness

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