The Marcinkiewicz-Zygmund law of large numbers for exchangeable arrays
Laurent Davezies, Xavier D'Haultfoeuille, Yannick Guyonvarch
TL;DR
This paper extends the Marcinkiewicz-Zygmund law of large numbers to exchangeable arrays, establishing new probabilistic convergence results in $L^r$ and almost surely, and deriving a law of iterated logarithm under weaker conditions.
Contribution
It introduces a law of large numbers and a law of iterated logarithm for exchangeable arrays, broadening the scope of classical probabilistic laws.
Findings
Law of large numbers in $L^r$ for exchangeable arrays
Almost sure convergence results for such arrays
A law of iterated logarithm under weaker moment conditions
Abstract
We show a Marcinkiewicz-Zygmund law of large numbers for jointly, dissociated exchangeable arrays, in () and almost surely. Then, we obtain a law of iterated logarithm for such arrays under a weaker moment condition than the existing one.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsProbability and Risk Models · Stochastic processes and statistical mechanics · Stochastic processes and financial applications