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A Functional Central Limit Theorem for Strong Mixing Stochastic Processes

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Abstract

This paper shows how the modern machinery for generating abstract empirical central limit theorems can be applied to arrays of dependent variables. It develops a bracketing approximation based on a moment inequality for sums of strong mixing arrays, in an effort to illustrate the sorts of difficulty that need to be overcome when adapting the empirical process theory for independent variables. Some suggestions for further development are offered. The paper is largely self-contained.

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  • Donald W.K. Andrews & David Pollard, 1990. "A Functional Central Limit Theorem for Strong Mixing Stochastic Processes," Cowles Foundation Discussion Papers 951, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:951
    Note: CFP 870.
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d09/d0951.pdf
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    1. Donald W.K. Andrews, 1989. "Asymptotics for Semiparametric Econometric Models: I. Estimation," Cowles Foundation Discussion Papers 908R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1990.
    2. Andrews, Donald W. K., 1991. "An empirical process central limit theorem for dependent non-identically distributed random variables," Journal of Multivariate Analysis, Elsevier, vol. 38(2), pages 187-203, August.
    3. Donald W.K. Andrews, 1989. "Asymptotics for Semiparametric Econometric Models: II. Stochastic Equicontinuity and Nonparametric Kernel Estimation," Cowles Foundation Discussion Papers 909R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1990.
    4. Yukich, J. E., 1986. "Rates of convergence for classes of functions: The non-i.i.d. case," Journal of Multivariate Analysis, Elsevier, vol. 20(2), pages 175-189, December.
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