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Coalescence time and second largest eigenvalue modulus in the monotone reversible case

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  • Leisen Fabrizio

    ()
    (Università di Modena e Reggio Emilia, Dipartimento di Matematica, Modena, Italy)

  • Mira Antonietta

    ()
    (Department of Economics, University of Insubria, Italy)

Abstract

If T is the coalescence time of the Propp and Wilson [15], perfect simulation algorithm, the aim of this paper is to show that T depends on the second largest eigenvalue modulus of the transition matrix of the underlying Markov chain. This gives a relationship between the ordering based on the speed of convergence to stationarity in total variation distance and the ordering de ned in terms of speed of coalescence in perfect simulation. Key words and phrases: Peskun ordering, Covariance ordering, Effciency ordering, MCMC, time-invariance estimating equations, asymptotic variance, continuous time Markov chains.

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Bibliographic Info

Paper provided by Department of Economics, University of Insubria in its series Economics and Quantitative Methods with number qf06011.

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Length: 14 pages
Date of creation: Jul 2006
Date of revision:
Handle: RePEc:ins:quaeco:qf06011

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