Semi-parametric inference based on adaptively collected data

Understand

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 semi-parametric context: estimating the parameter vector of a generalized linear regression model contaminated by a non-parametric 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.