Sampling With Replacement vs Poisson Sampling: A Comparative Study in Optimal Subsampling

Faced with massive data, subsampling is a commonly used technique to improve computational efficiency, and using nonuniform probabilities an effective approach estimation efficiency. For often implemented replacement or through Poisson subsampling. However, no rigorous investigation has been performed study the difference between two procedures such as their efficiency convenience. This paper performs comparative on these different sampling procedures. In context of maximizing general target function, we first derive asymptotic distributions for estimators obtained from The results show that may have higher Based both subsampling, optimal minimize variance functions estimators. These further reveal similarities differences theoretical characterizations comparisons provide guidance select more appropriate in practice. Furthermore, practically implementable algorithms are proposed based structural results, which evaluated empirical analyses.