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Laws of large numbers for dependent non-identically distributed random variables

Andrews, Donald W. K. (1988) Laws of large numbers for dependent non-identically distributed random variables. Econometric Theory, 4 (3). pp. 458-467. ISSN 0266-4666.

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This paper provides L^1 and weak laws of large numbers for uniformly integrable L^1-mixingales. The L^1-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, φ(.), ρ(.), and α(.) mixing, autoregressive moving average, infinite-order moving average, near epoch dependent, L^1-near epoch dependent, and mixingale sequences and triangular arrays. The random variables need not possess more than one finite moment and the L^1-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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Additional Information:© 1988 Cambridge University Press. I would like to thank the referees, Hal White, and In Choi for helpful comments, the California Institute of Technology for their hospitality while this research was undertaken, and the Alfred P. Sloan Foundation and the National Science Foundation for their financial support through a Research Fellowship and Grant SES-8618617, respectively. Formerly SSWP 645.
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Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:Martingales, Autoregressive moving average, Economic theory, Law of large numbers, Economic modeling, Economic models, Estimators, Random variables, Zero, Theoretical econometrics
Issue or Number:3
Record Number:CaltechAUTHORS:20171109-164301183
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83122
Deposited By: Jacquelyn Bussone
Deposited On:16 Nov 2017 22:27
Last Modified:03 Oct 2019 19:02

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