  Sequential data collection has emerged as a widely adopted technique for
enhancing the efficiency of data gathering processes. Despite its advantages,
such data collection mechanism often introduces complexities to the statistical
inference procedure. For instance, the ordinary least squares (OLS) estimator
in an adaptive linear regression model can exhibit non-normal asymptotic
behavior, posing challenges for accurate inference and interpretation. In this
paper, we propose a general method for constructing debiased estimator which
remedies this issue. It makes use of the idea of adaptive linear estimating
equations, and we establish theoretical guarantees of asymptotic normality,
supplemented by discussions on achieving near-optimal asymptotic variance. A
salient feature of our estimator is that in the context of multi-armed bandits,
our estimator retains the non-asymptotic performance of the least square
estimator while obtaining asymptotic normality property. Consequently, this
work helps connect two fruitful paradigms of adaptive inference: a)
non-asymptotic inference using concentration inequalities and b) asymptotic
inference via asymptotic normality.
