| Título: | Asymptotic variance of functionals of discrete-time Markov chains via the Drazin inverse. |
| Autores: |
Spitzner, Dan J.; Department of Statistics (0439), Virginia Tech, Blacksburg, VA Boucher, Thomas R; Department of Mathematics, Plymouth State |
| Fecha: | 2007-01-01 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: | General state space Markov chains; $f$-regularity; Markov chain central limit theorem; Drazin inverse; fundamental matrix; asymptotic variance |
| Descripción: | 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. |
| Idioma: | No aplica |
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