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Central limit theorems under weak dependence

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  • Bradley, Richard C.

Abstract

This article is motivated by a central limit theorem of Ibragimov for strictly stationary random sequences satisfying a mixing condition based on maximal correlations. Here we show that the mixing condition can be weakened slightly, and construct a class of stationary random sequences covered by the new version of the theorem but not Ibragimov's original version. Ibragimov's theorem is also extended to triangular arrays of random variables, and this is applied to some kernel-type estimates of probability density.

Suggested Citation

  • Bradley, Richard C., 1981. "Central limit theorems under weak dependence," Journal of Multivariate Analysis, Elsevier, vol. 11(1), pages 1-16, March.
    • Handle: RePEc:eee:jmvana:v:11:y:1981:i:1:p:1-16
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    Cited by:

    1. Alexander Varypaev, 2024. "Asymptotic Form of the Covariance Matrix of Likelihood-Based Estimator in Multidimensional Linear System Model for the Case of Infinity Number of Nuisance Parameters," Mathematics, MDPI, vol. 12(3), pages 1-22, February.
    2. Sergey Utev & Magda Peligrad, 2003. "Maximal Inequalities and an Invariance Principle for a Class of Weakly Dependent Random Variables," Journal of Theoretical Probability, Springer, vol. 16(1), pages 101-115, January.
    3. Martin Spiess & Pascal Jordan & Mike Wendt, 2019. "Simplified Estimation and Testing in Unbalanced Repeated Measures Designs," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 212-235, March.
    4. Aneiros-Pérez, Germán, 2002. "On bandwidth selection in partial linear regression models under dependence," Statistics & Probability Letters, Elsevier, vol. 57(4), pages 393-401, May.
    5. Gonzalo Perera, 1997. "Geometry of $$\mathbb{Z}^d $$ and the Central Limit Theorem for Weakly Dependent Random Fields," Journal of Theoretical Probability, Springer, vol. 10(3), pages 581-603, July.
    6. Furrer, Reinhard, 2005. "Covariance estimation under spatial dependence," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 366-381, June.
    7. Daouia, Abdelaati & Stupfler, Gilles & Usseglio-Carleve, Antoine, 2022. "Inference for extremal regression with dependent heavy-tailed data," TSE Working Papers 22-1324, Toulouse School of Economics (TSE), revised 29 Aug 2023.

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