Semiparametric inference based on adaptively collected data
Licong Lin, Koulik Khamaru, Martin J. Wainwright
The Annals of Statistics · 2025 · Volume 53 · Issue 3
Abstract
Many standard estimators, when applied to adaptively collected data, fail to be asymptotically normal, thereby complicating the construction of confidence intervals. We address this challenge in a semiparametric context: estimating the parameter vector of a generalized linear regression model contaminated by a nonparametric nuisance component. We construct suitably weighted estimating equations that account for adaptivity in data collection and provide conditions under which the associated estimates are asymptotically normal. Our results characterize the degree of “explorability” required for asymptotic normality to hold. For the simpler problem of estimating a linear functional, we provide similar guarantees under much weaker assumptions. We illustrate our general theory with concrete consequences for various problems, including standard linear bandits and sparse generalized bandits, and compare with other methods via simulation studies.
Keywords
6208, 62E20, adaptive data collection, generalized linear model, semiparametric inference, two-stage weighted Z-estimator
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