Semiparametric inference based on adaptively collected data
研究了在自适应收集数据下，如何对含有非参数干扰项的广义线性回归模型进行参数估计，并构造渐近正态的置信区间，适用于线性bandit等场景。
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.