Title: On variance estimation in online problems
Authors: Man Fung Leung - University of Illinois Urbana-Champaign (United States)
Kin Wai Chan - The Chinese University of Hong Kong (Hong Kong) [presenting]
Abstract: Online problems arise naturally in many fields of statistics. On top of them, modern computing allows intractable offline problems to be approached with online techniques. Nevertheless, variance estimation in online problems remains largely offline, which limits the practical value of inference-based techniques. We propose a general framework to construct efficient long-run variance estimators in online problems. The contributions lie in three aspects. Statistically, we derive the first set of sufficient conditions for $O(1)$-time or $O(1)$-space update, which allows our framework to generate online estimators that uniformly dominate existing alternatives. Computationally, we introduce mini-batch estimation to accelerate online estimators in practice. Implementation issues such as automatic optimal parameters selection are discussed. Practically, we demonstrate the possibility to use recursive (online and mini-batch) estimators in convergence diagnostics and learning rate tuning. We also illustrate the strength of our estimators in some standard online problems such as change-point detection and confidence interval construction.