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

#### P. Collet, D. Duarte, A. Galves

2005, v.11, Issue 3, 443-464

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.

Keywords: bootstrap,chains of infinite order,canonical Markovapproximations,central limit theorem