A Central Limit Theorem For Empirical Quantiles in the Markov Chain Setting

Peter W. Glynn () and Shane G. Henderson ()
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Peter W. Glynn: Stanford University
Shane G. Henderson: Cornell University

A chapter in Advances in Modeling and Simulation, 2022, pp 211-238 from Springer

Abstract: Abstract We provide a new proof of a central limit theorem for empirical quantiles in the positive-recurrent Markov process setting under conditions that are essentially tight. We also establish the validity of the method of nonoverlapping batch means with a fixed number of batches for interval estimation of the quantile. The conditions of these results are likely to be difficult to verify in practice, and so we also provide more easily verified sufficient conditions.

Keywords: Quantile estimation; Harris processes; Regenerative processes; Markov chain Monte Carlo (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-10193-9_11

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DOI: 10.1007/978-3-031-10193-9_11

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