Asymptotic stability of the bootstrap sample mean

The asymptotic distribution of the bootstrap sample mean depends on the resampling intensity. This paper explores the sensitivity of that distribution against different resampling intensities. It is generally assumed that small resampling sizes make the bootstrap work. However, we will show that the bootstrap mean can only be highly unstable for small resampling intensities. Our setup considers resampling from a triangular array of row-wise independent and identically distributed random variables satisfying the Central Limit Theorem.