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Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables


  • Andrews, Donald W. K.


This paper provides L1 and weak laws of large numbers for uniformly integrable L1-mixingales. The L1-mixingale condition is a condition of asymptotic weak temporal dependence that is weaker than most conditions considered in the literature. Processes covered by the laws of large numbers include martingale difference, ø(·), Ï (·), and α(·) mixing, autoregressive moving average, infinite-order moving average, near epoch dependent, L1-near epoch dependent, and mixingale sequences and triangular arrays. The random variables need not possess more than one finite moment and the L1-mixingale numbers need not decay to zero at any particular rate. The proof of the results is remarkably simple and completely self-contained.
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Suggested Citation

  • Andrews, Donald W. K., 1987. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Working Papers 645, California Institute of Technology, Division of the Humanities and Social Sciences.
  • Handle: RePEc:clt:sswopa:645

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