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Bootstrap in Markov-sequences based on estimates of transition density. (English) Zbl 0714.62036

Summary: We develop a bootstrap method in Markov-sequences. This method is based on kernel estimates of the transition density of the Markov-sequence. It is shown that the bootstrap estimate of the variance of a statistic which is a function of means, is consistent. We also show that the bootstrap distributions of mean-like statistics and von Mises differentiable statistics converge to appropriate normal distributions. A few simulation results are reported to illustrate the discussion.

MSC:

62G09 Nonparametric statistical resampling methods
62M05 Markov processes: estimation; hidden Markov models
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