Offline estimators are often inadequate for real-time applications. Nevertheless, many online estimators are found by sacrificing some statistical efficiency. This paper presents a general framework to understand and construct efficient nonparametric estimators for online problems. Statistically, we choose long-run variance as an exemplary estimand and derive the first set of sufficient conditions for O(1)-time or O(1)-space update, which allows methodological generation of estimators. Our asymptotic theory shows that the generated estimators dominate existing alternatives. Computationally, we introduce mini-batch estimation to accelerate online estimators for real-time applications. Implementation issues such as automatic optimal parameters selection are discussed. Practically, we demonstrate how to use our framework with recent development in change point detection, causal inference, and stochastic approximation. We also illustrate the strength of our estimators in some classical problems such as Markov chain Monte Carlo convergence diagnosis and confidence interval construction.
翻译：离线估计器往往不足以实时应用。 然而,许多在线估计器都是通过牺牲某些统计效率而发现的。 本文为理解和构建高效的非参数估计器提供了一个总体框架, 用于解决在线问题。 从统计上看, 我们选择长期差异作为堪称典范的估计值, 并为O(1)-time或O(1)-space更新得出第一套足够条件, 从而允许在方法上生成估计器。 我们的无症状理论显示, 生成的估计器主宰了现有的替代物。 计算上, 我们引入了小型估计, 以加速实时应用的在线估计器。 讨论了自动最佳参数选择等执行问题。 实际上, 我们展示了如何利用我们的框架来进行最近的变化点检测、 因果关系和随机近似。 我们还展示了我们估算器在一些传统问题中的力量, 比如Markov 链 蒙特卡洛 趋同 诊断和信任度间建构等 。
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