Bootstrapping Markov chains: Countable case

DOI10.1016/0378-3758(92)90002-AzbMath0765.62078MaRDI QIDQ1205467

Cheng-Der Fuh, Krishna B. Athreya

Publication date: 1 April 1993

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

zbMATH Keywords

transition probability matrixcentral limit theoremmaximum likelihood estimatestationary probabilitybootstrap methodscountably infinite state spacedouble array of Markov chainshitting time distributionirreducible, aperiodic and positive recurrent Markov chainweak law

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Markov processes: estimation; hidden Markov models (62M05) Nonparametric statistical resampling methods (62G09) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10)

Related Items (25)

Bootstrap uniform central limit theorems for Harris recurrent Markov chains ⋮ Regeneration-based bootstrap for Markov chains ⋮ Regenerative block-bootstrap for Markov chains ⋮ Second-order properties of regeneration-based bootstrap for atomic Markov chains ⋮ Renewal type bootstrap for Markov chains ⋮ Renewal type bootstrap for increasing degree \(U\)-process of a Markov chain ⋮ The threshold bootstrap and threshold jackknife ⋮ Confidence intervals for the Shapley-Shubik power index in Markovian games ⋮ Balanced importance resampling for Markov chains ⋮ A simple nonparametric method to estimate the expected time to cross a threshold ⋮ Relevant states and memory in Markov chain bootstrapping and simulation ⋮ Bootstrapping the autocorrelation coefficient of finite Markov chains ⋮ Balanced resampling for bootstrapping finite state markov chains ⋮ Bootstrap and Bayesian bootstrap clones for censored Markov chains ⋮ A block bootstrap comparison for sparse chains ⋮ Asymptotic Inference for Waiting Times and Patiences in Queues with Abandonment ⋮ Approximating multivariate Markov chains for bootstrapping through contiguous partitions ⋮ Bootstrap methods for dependent data: a review ⋮ Second order optimality of stationary bootstrap ⋮ Approximate regenerative-block bootstrap for Markov chains ⋮ Local stationarity and time-inhomogeneous Markov chains ⋮ Regeneration-based statistics for Harris recurrent Markov chains ⋮ Countable state Markov process bootstrap ⋮ On Mixture Periodic Vector Autoregressive Models ⋮ On the moving block bootstrap under long range dependence

Cites Work

• Unnamed Item
• Bootstrapping general empirical measures
• Strong law for the bootstrap
• Bootstrap of the mean in the infinite variance case
• Some asymptotic theory for the bootstrap
• On the asymptotic accuracy of Efron's bootstrap
• Bootstrap methods: another look at the jackknife
• SOME ASYMPTOTIC DISTRIBUTION THEORY FOR MARKOV CHAINS WITH A DENUMERABLE NUMBER OF STATES
• The Lindeberg-Levy Theorem for Martingales
• On the range of recurrent Markov chains
• On the range of recurrent Markov chains

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