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

Andrews, Donald K. (1987) Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables. Social Science Working Paper, 645. California Institute of Technology , Pasadena, CA. (Unpublished)

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This paper provides L` 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, Φ(.), ρ(.) 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 moment finite 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.

Item Type:Report or Paper (Discussion Paper)
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Additional Information:I would like to thank 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 number SES-8618617, respectively.
Group:Social Science Working Papers
Funding AgencyGrant Number
Alfred P. Sloan FoundationUNSPECIFIED
NSF Graduate Research FellowshipUNSPECIFIED
Subject Keywords:Martingales, Autoregressive moving average, Economic theory, Law of large numbers, Economic modeling, Economic models, Estimators, Random variables, Zero, Theoretical econometrics
Series Name:Social Science Working Paper
Issue or Number:645
Record Number:CaltechAUTHORS:20170908-163911965
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81278
Deposited By: Jacquelyn Bussone
Deposited On:11 Sep 2017 18:39
Last Modified:03 Oct 2019 18:40

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