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arXiv 2407.13446stat.ME
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用于快速统计推断的子采样一步估计

Subsampled One-Step Estimation for Fast Statistical Inference

Miaomiao Su, Ruoyu Wang

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AI总结：

本文提出子采样一步（SOS）估计方法，利用渐近展开弥补子采样估计的效率损失，在保持计算高效的同时实现接近全数据估计的收敛速度和统计推断性能。

摘要：

子采样是缓解大规模数据集计算负担的有效方法。然而，与基于完整数据集的估计量相比，现有子采样估计量在估计效率上存在显著损失。具体而言，现有子采样估计量的收敛速度通常为$n^{-1/2}$而非$N^{-1/2}$，其中$n$和$N$分别表示子样本量和完整数据量。本文提出了一种子采样一步（SOS）方法，利用子采样估计量和完整数据估计量的渐近展开来减轻估计效率损失。所得的SOS估计量计算效率高，并实现了$\max\{n^{-1}, N^{-1/2}\}$的快速收敛速度，而非$n^{-1/2}$。我们建立了SOS估计量的渐近分布，该分布在一般情况下可以是非正态的，并在该渐近分布的基础上构建置信区间。此外，我们证明了当$n / \sqrt{N} \to \infty$时，SOS估计量是渐近正态的，并且等价于基于完整数据的估计量。通过模拟研究和真实数据分析展示了SOS估计量的有限样本表现。数值结果表明，SOS估计量的计算效率几乎与均匀子采样估计量相当，同时实现了与基于完整数据的估计量相似的估计效率。

英文摘要：

Subsampling is an effective approach to alleviate the computational burden associated with large-scale datasets. Nevertheless, existing subsampling estimators incur a substantial loss in estimation efficiency compared to estimators based on the full dataset. Specifically, the convergence rate of existing subsampling estimators is typically $n^{-1/2}$ rather than $N^{-1/2}$, where $n$ and $N$ denote the subsample and full data sizes, respectively. This paper proposes a subsampled one-step (SOS) method to mitigate the estimation efficiency loss utilizing the asymptotic expansions of the subsampling and full-data estimators. The resulting SOS estimator is computationally efficient and achieves a fast convergence rate of $\max\{n^{-1}, N^{-1/2}\}$ rather than $n^{-1/2}$. We establish the asymptotic distribution of the SOS estimator, which can be non-normal in general, and construct confidence intervals on top of the asymptotic distribution. Furthermore, we prove that the SOS estimator is asymptotically normal and equivalent to the full data-based estimator when $n / \sqrt{N} \to \infty$.Simulation studies and real data analyses were conducted to demonstrate the finite sample performance of the SOS estimator. Numerical results suggest that the SOS estimator is almost as computationally efficient as the uniform subsampling estimator while achieving similar estimation efficiency to the full data-based estimator.

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