A law of large numbers result for a bifurcating process with an infinite moving average representation

DOI10.1016/j.spl.2011.09.012zbMath1230.60032OpenAlexW2084880883MaRDI QIDQ654489

Tamer Elbayoumi, Jeffrey T. Terpstra

Publication date: 28 December 2011

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spl.2011.09.012

zbMATH Keywords

binary treelaw of large numbersbifurcating processcovariance inequalitygeometric decay

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Strong limit theorems (60F15)

Related Items (7)

On the Asymptotic Distribution of a Weighted Least Absolute Deviation Estimate for a Bifurcating Autoregressive Process ⋮ The strong law of large numbers for non homogeneous M-bifurcating Markov chains indexed by a M-branch Cayley tree ⋮ Strong law of large numbers of the delayed sums for Markov Chains indexed by a Cayley tree ⋮ Equivalent properties for the bifurcating Markov chains indexed by a binary tree ⋮ A class of strong deviation theorems for the random fields associated with bifurcating Markov chains indexed by a binary tree ⋮ Weighted L₁-estimates for the First-order Bifurcating Autoregressive Model ⋮ Estimation for a first-order bifurcating autoregressive process with heavy-tail innovations

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