Bootstrap Central Limit Theorem for Chains of Infinite Order via Markov Approximations

Details Bootstrap Central Limit Theorem for Chains of Infinite Order via Markov Approximations Bootstrap Central Limit Theorem for Chains of Infinite Order via Markov Approximations

2005-05-11

arxiv.org/abs/math/0505232v1

Mathematics

Probability

26 pages, TeX file

Scientific paper

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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