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Asymptotic variance of functionals of discrete-time Markov chains via the Drazin inverse.


 
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1. Title Title of document Asymptotic variance of functionals of discrete-time Markov chains via the Drazin inverse.
 
2. Creator Author's name, affiliation, country Dan J. Spitzner; Department of Statistics (0439), Virginia Tech, Blacksburg, VA
 
2. Creator Author's name, affiliation, country Thomas R Boucher; Department of Mathematics, Plymouth State
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) General state space Markov chains; $f$-regularity; Markov chain central limit theorem; Drazin inverse; fundamental matrix; asymptotic variance
 
4. Description Abstract We consider a $\psi$-irreducible, discrete-time Markov chain on a general state space with transition kernel $P$. Under suitable conditions on the chain, kernels can be treated as bounded linear operators between spaces of functions or measures and the Drazin inverse of the kernel operator $I - P$ exists. The Drazin inverse provides a unifying framework for objects governing the chain. This framework is applied to derive a computational technique for the asymptotic variance in the central limit theorems of univariate and higher-order partial sums. Higher-order partial sums are treated as univariate sums on a `sliding-window' chain. Our results are demonstrated on a simple AR(1) model and suggest a potential for computational simplification.
 
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7. Date (YYYY-MM-DD) 2007-04-24
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1262
 
10. Identifier Digital Object Identifier 10.1214/ECP.v12-1262
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 12
 
12. Language English=en
 
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