大数据M估计的近最优捕获-再捕获抽样与经验似然加权估计
Nearly optimal capture-recapture sampling and empirical likelihood weighting estimation for M-estimation with big data
摘要：
子采样技术可以降低处理大数据的计算成本。实际的二次抽样计划通常包括初始均匀抽样和细化抽样。对于子样本，大数据推断通常建立在逆概率加权（IPW）上，当概率权重接近零时，IPW变得不稳定，并且不能包含辅助信息。首先，我们考虑捕获-再捕获采样，它结合了初始均匀采样和第二泊松采样。在这种抽样方案下，我们提出了一个经验似然加权（ELW）估计方法的M-估计参数。其次，基于ELW方法，我们构造了一个近似最优的捕获-再捕获抽样方案，该方案平衡了估计效率和计算成本。第三，我们得出的方法来确定最小的样本量，建议的抽样和估计方法产生的估计保证精度。我们的ELW方法通过规避使用逆概率来克服IPW的不稳定性，并利用辅助信息，包括大数据的大小和某些样本矩。我们表明，建议ELW方法产生更有效的估计比IPW，导致更有效的最优抽样计划和更经济的样本量的一个预先指定的估计精度。这些优点通过仿真研究和实际数据分析得到证实。
英文摘要：
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.
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