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Weak Laws of Large Numbers for Dependent Random Variables

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  • Robert M. De Jong

Abstract

In this paper we will prove several weak laws of large numbers for dependent random variables. The weak dependence concept that is used is the mixingale concept. From the weak laws of large numbers for triangular arrays of mixingale random variables, weak laws for mixing and near epoch dependent random variables follow. Features of the weak laws of large numbers that are proven here is that they impose tradeoff conditions between dependence and trending of the summands.

Suggested Citation

  • Robert M. De Jong, 1998. "Weak Laws of Large Numbers for Dependent Random Variables," Annals of Economics and Statistics, GENES, issue 51, pages 209-225.
    • Handle: RePEc:adr:anecst:y:1998:i:51:p:209-225
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    File URL: http://www.jstor.org/stable/20076144
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    Cited by:

    1. Kanaya, Shin, 2017. "Convergence Rates Of Sums Of Α-Mixing Triangular Arrays: With An Application To Nonparametric Drift Function Estimation Of Continuous-Time Processes," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1121-1153, October.
    2. de Castro, Luciano & Galvao, Antonio F. & Kaplan, David M. & Liu, Xin, 2019. "Smoothed GMM for quantile models," Journal of Econometrics, Elsevier, vol. 213(1), pages 121-144.
    3. Christian Gourieroux & Joann Jasiak, 2022. "Long Run Risk in Stationary Structural Vector Autoregressive Models," Papers 2202.09473, arXiv.org.
    4. Joann Jasiak & Aryan Manafi Neyazi, 2023. "GCov-Based Portmanteau Test," Papers 2312.05373, arXiv.org.
    5. de Castro, Luciano & Galvao, Antonio F. & Kaplan, David M. & Liu, Xin, 2019. "Smoothed GMM for quantile models," Journal of Econometrics, Elsevier, vol. 213(1), pages 121-144.

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