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Some Estimates for the Rate of Convergence in the Multidimensional Central Limit Theorem for Homogeneous Markov Chains
Author(s) -
Gharib M.
Publication year - 1998
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00010
Subject(s) - mathematics , central limit theorem , markov chain , homogeneous , limit (mathematics) , character (mathematics) , moment (physics) , rate of convergence , convergence (economics) , markov process , pure mathematics , mathematical analysis , statistics , combinatorics , channel (broadcasting) , physics , geometry , classical mechanics , economic growth , electrical engineering , economics , engineering
This paper obtains some estimates for the rate of convergence in the multi‐dimensional central limit theorem for vector‐valued functions of a homogeneous Markov chain without assuming the finiteness of their absolute third moment. These estimates have a universal character and generalize the results that hold when the third moments are finite.