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Mixingale and physical dependence equality with applications

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  • Hill, Jonathan B.

Abstract

We prove Wu (2005)’s physical dependence and Wu and Min (2005)’s Lp-weak dependence properties are asymmetrically equivalent to the adapted mixingale property (each implying the other with possibly different memory decay rates), and identical under geometric memory. We apply the result to two unique cases: (i) a new Gaussian approximation theory for high dimensional near epoch dependent processes, and (ii) a new maximal moment inequality for Lp-physical dependent arrays when 1

Suggested Citation

  • Hill, Jonathan B., 2025. "Mixingale and physical dependence equality with applications," Statistics & Probability Letters, Elsevier, vol. 221(C).
    • Handle: RePEc:eee:stapro:v:221:y:2025:i:c:s0167715225000252
    DOI: 10.1016/j.spl.2025.110380
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