# Nearly optimal capture-recapture sampling and empirical likelihood weighting estimation for M-estimation with big data

arXiv: https://arxiv.org/abs/2209.04569 · HTML: https://mlsanity.com/paper/2209.04569/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2022.

## Built on by (most cited first, 1 of 1)

- [How important is Recall for Measuring Retrieval Quality?](https://mlsanity.com/paper/2512.20854/) (2025)

## Abstract (arXiv)

Subsampling techniques can reduce the computational costs of processing big data. Practical subsampling plans typically involve initial uniform sampling and refined sampling. With a subsample, big data inferences are generally built on the inverse probability weighting (IPW), which becomes unstable when the probability weights are close to zero and cannot incorporate auxiliary information. First, we consider capture-recapture sampling, which combines an initial uniform sampling with a second Poisson sampling. Under this sampling plan, we propose an empirical likelihood weighting (ELW) estimation approach to an M-estimation parameter. Second, based on the ELW method, we construct a nearly optimal capture-recapture sampling plan that balances estimation efficiency and computational costs. Third, we derive methods for determining the smallest sample sizes with which the proposed sampling-and-estimation method produces estimators of guaranteed precision. Our ELW method overcomes the instability of IPW by circumventing the use of inverse probabilities, and utilizes auxiliary information including the size and certain sample moments of big data. We show that the proposed ELW method produces more efficient estimators than IPW, leading to more efficient optimal sampling plans and more economical sample sizes for a prespecified estimation precision. These advantages are confirmed through simulation studies and real data analyses.