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Convergence of moments in a Markov-chain central limit theorem

Abstract:

Let (Xi)i=0∞ be a V-uniformly ergodic Markov chain on a general state space, and let π be its stationary distribution. For g : χ → R, define It is shown that if |g| ≤ V1/n for a positive integer n, then ExWk(g)n converges to the n-th moment of a normal random variable with expectation 0 and variance This extends the existing Markov-chain central limit theorems, according to which expectations of bounded functionals of Wk(g) converge. We also derive nonasymptotic bounds for the error in approx...

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Published

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Institution:
University of Oxford
Department:
Oxford, MPLS, Statistics
Role:
Author
Journal:
INDAGATIONES MATHEMATICAE-NEW SERIES
Volume:
12
Issue:
4
Pages:
533-555
Publication date:
2001-12-17
DOI:
ISSN:
0019-3577
URN:
uuid:4093f2f3-60bb-4a1e-8bea-19c296ee8eb2
Source identifiers:
97800
Local pid:
pubs:97800
Language:
English

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