General Weak Laws of Large Numbers for Bootstrap Sample Means

Abstract

For bootstrap sample means resulting from a sequence {X n , n ≥ 1} of random variables, very general weak laws of large numbers are 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. In general, no moment conditions are imposed on the {X n , n ≥ 1}. Examples are provided which illustrate the sharpness of the main results.