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. 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.
翻译:许多标准估计器在应用到适应性收集的数据时,没有做到尽可能正常,从而使得建立信任间隔的构建复杂化。我们从半参数的角度来应对这一挑战:估计受非参数性扰动部分污染的普遍线性回归模型的参数矢量。我们构建了适当的加权估计方程,其中考虑到数据收集的适应性,提供了相关估计在同样情况下也具有同样正常的条件。我们的结果说明了保持无症状性正常所需的“可探测性”程度。关于估算线性功能这一较简单的问题,我们在较弱的假设下提供了类似的保障。我们用模拟研究来说明我们的一般理论,对各种问题,包括标准的线性强盗和稀少的普遍强盗,具有具体后果,并与其他方法进行比较。</s>