A block bootstrap comparison for sparse chains

摘要

In this paper we apply the sequential bootstrap method proposed by Collet et al. [Bootstrap Central Limit theorem for chains of infinite order via Markov approximations, Markov Processes and Related Fields 11 (3) (2005), pp. 443-464] to estimate the variance of the empirical mean of a special class of chains of infinite order called sparse chains. For this process, we show that we are able to compute numerically the true value of the standard error with any fixed error.rnOur main goal is to present a comparison, for sparse chains, among sequential bootstrap, the block bootstrap method proposed by Kunsch [Thejackknife and the Bootstrap for general stationary observations, Ann. Statist. 17 (1989), pp. 1217-1241] and improved by Liu and Singh [Moving blocks jackknife and Bootstrap capture week dependence, in Exploring the limits of the Bootstrap, R. Lepage and L. Billard, eds., Wiley, New York, 1992, pp. 225-248] and the bootstrap method proposed by Buehlmann [Blockwise bootstrapped empirical process for stationary sequences, Ann. Statist. 22 (1994), pp. 995-1012].