为神经估计器提供理论保证，解决其缺乏统计可靠性的问题。
Theoretical guarantees for neural estimators in parametric statistics
- 将估计误差分解为可分别分析的若干项，逐项证明收敛性。
- 在常见应用中验证了各条件成立，确保整体风险趋近于零。
- 适用于多种网络结构，为新方法提供理论验证框架。
神经估计器是基于模拟的参数估计方法，通过神经网络直接建立样本到参数向量的映射，具备深度学习中丰富的网络架构与高效训练优势。这类方法具有摊销特性：训练完成后，对任意新数据集的推理几乎无额外计算成本。尽管已有大量文献在模拟和实际应用中展示了其优异性能，但至今缺乏理论上的统计保障。本文通过将神经估计器的风险分解为多个可独立分析的项，提出了易于检验的假设条件，确保每项收敛至零，并在神经估计器的典型应用场景中验证了这些条件的成立。研究结果为更广泛的模型架构和估计问题提供了通用的理论保障推导方法。
原文摘要 · Abstract (English)
Neural estimators are simulation-based estimators for the parameters of a family of statistical models, which build a direct mapping from the sample to the parameter vector. They benefit from the versatility of available network architectures and efficient training methods developed in the field of deep learning. Neural estimators are amortized in the sense that, once trained, they can be applied to any new data set with almost no computational cost. While many papers have shown very good performance of these methods in simulation studies and real-world applications, so far no statistical guarantees are available to support these observations theoretically. In this work, we study the risk of neural estimators by decomposing it into several terms that can be analyzed separately. We formulate easy-to-check assumptions ensuring that each term converges to zero, and we verify them for popular applications of neural estimators. Our results provide a general recipe to derive theoretical guarantees also for broader classes of architectures and estimation problems.
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