BLOCK BOOTSTRAP CONSISTENCY UNDER WEAK ASSUMPTIONS
放宽了块自助法（移动块、循环块和固定自助法）对近邻相依函数样本均值有效所需的条件，证明在保证原过程服从中心极限定理的最弱条件下自助法仍一致，并推广到随机不等块长和泛函中心极限定理。
This paper weakens the size and moment conditions needed for typical block bootstrap methods (i.e., the moving blocks, circular blocks, and stationary bootstraps) to be valid for the sample mean of Near-Epoch-Dependent (NED) functions of mixing processes; they are consistent under the weakest conditions that ensure the original NED process obeys a central limit theorem (CLT), established by De Jong (1997, Econometric Theory 13(3), 353–367). In doing so, this paper extends De Jong’s method of proof, a blocking argument, to hold with random and unequal block lengths. This paper also proves that bootstrapped partial sums satisfy a functional CLT (FCLT) under the same conditions.