A central limit theorem for bootstrap sample sums from non-i.i.d. models

作者：Rosalsky Andrew^*; Li Deli

来源：Journal of Statistical Planning and Inference, 2017, 180: 69-80.

DOI：10.1016/j.jspi.2016.08.002

• Bootstrap samples
• Central limit theorem
• Almost sure convergence
• Random bootstrap sample size

For bootstrap sample sums resulting from a sequence of random variables {X-n, n >= 1}, a very general central limit theorem is established. The random variables {X-n, n >= 1} do not need to be independent or identically distributed or to be of any particular dependence structure. Furthermore, no conditions, including moment conditions, are imposed in general on the marginal distributions of the {X-n, n >= 1}. As a special case of the main result, a result of Liu (1988) concerning independent but non -identically distributed {X-n, n >= 1} is extended to a larger class of parent sequences. Aversion of the main result is also presented wherein the bootstrap sample sums have random bootstrap sample sizes.

• 出版日期2017-1