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Markov chain Monte Carlo estimation of quantiles. (English) Zbl 1329.62363

Summary: We consider quantile estimation using Markov chain Monte Carlo and establish conditions under which the sampling distribution of the Monte Carlo error is approximately Normal. Further, we investigate techniques to estimate the associated asymptotic variance, which enables construction of an asymptotically valid interval estimator. Finally, we explore the finite sample properties of these methods through examples and provide some recommendations to practitioners.

MSC:

62M05 Markov processes: estimation; hidden Markov models
60J22 Computational methods in Markov chains
65C60 Computational problems in statistics (MSC2010)

Software:

mcmcse; Gibbsit
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Full Text: DOI arXiv Euclid

References:

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