Bootstrap Central Limit Theorem for Chains of Infinite Order via Markov Approximations
P. Collet, D. Duarte, A. Galves
TL;DR
This paper introduces a bootstrap method for chains of infinite order using Markov approximations, establishing a CLT for the bootstrap estimator of the sample mean.
Contribution
It develops a new bootstrap approach for infinite order chains based on Markov approximations, leading to a CLT for the bootstrap sample mean.
Findings
Establishes a bootstrap CLT for chains of infinite order
Provides convergence rates for Markov approximations
Validates the bootstrap method for sample mean estimation
Abstract
We present a new approach to the bootstrap for chains of infinite order taking values on a finite alphabet. It is based on a sequential Bootstrap Central Limit Theorem for the sequence of canonical Markov approximations of the chain of infinite order. Combined with previous results on the rate of approximation this leads to a Central Limit Theorem for the bootstrapped estimator of the sample mean which is the main result of this paper.
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Taxonomy
TopicsBayesian Methods and Mixture Models · Markov Chains and Monte Carlo Methods · Statistical Methods and Inference