论文标题
在线问题中统计推断的原则
Principles of Statistical Inference in Online Problems
论文作者
论文摘要
为了研究长期差异估计器面临的统计和计算效率的困境，我们提出了以二次形式和一些在线推理原则的内核权重分解。这些建议使我们能够表征有效的在线长期差异估计器。我们的渐近理论和模拟表明，这种原理驱动的方法导致在线估计器的均匀平方误差比所有现有作品都均匀。我们还讨论了实用的增强功能，例如迷你批次和自动更新，以处理快速流数据和最佳参数调整。除差异估计之外，我们考虑了在线分位回归，在线变更点检测，马尔可夫链蒙特卡洛收敛诊断和随机近似的背景下的建议。当我们将原理驱动方差估计器应用于原始和修改的推理程序时，可以观察到计算成本和有限样本统计属性的实质性改善。
To investigate a dilemma of statistical and computational efficiency faced by long-run variance estimators, we propose a decomposition of kernel weights in a quadratic form and some online inference principles. These proposals allow us to characterize efficient online long-run variance estimators. Our asymptotic theory and simulations show that this principle-driven approach leads to online estimators with a uniformly lower mean squared error than all existing works. We also discuss practical enhancements such as mini-batch and automatic updates to handle fast streaming data and optimal parameters tuning. Beyond variance estimation, we consider the proposals in the context of online quantile regression, online change point detection, Markov chain Monte Carlo convergence diagnosis, and stochastic approximation. Substantial improvements in computational cost and finite-sample statistical properties are observed when we apply our principle-driven variance estimator to original and modified inference procedures.
