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Estimation Bias Adjustment for Adaptively Collected Data
Wang, Tong
Wang, Tong
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Thesis/Dissertation
Date
2022
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Statistics
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http://dx.doi.org/10.34944/dspace/8007
Abstract
In many scientific experiments involving the multi-arm bandits, the data is collectedand are genuinely dependent. As a result, many commonly used the statistical
inference methods could be problematic. For example, the ordinary least square
estimator, which is widely used in the regression literature, will produce a biased
estimator in the contextual disjoint linear models. As a result, any further statistical
inference methods such as the hypothesis testing and confidence interval based on this
biased estimator could be either invalid or conservative. We develop approaches in
two stages: pre-data bias mitigation (pre-BM) and post-data bias mitigation (post-
BM) to correct this. In Chapter 2, we propose an alternative approach named the
randomized Multi-Arm Bandits (rMAB) that combines a randomization step with a
chosen MAB algorithm. The proposed rMAB can achieve the optimal regret asymptotically
if choosing randomization probability appropriately. It is shown numerically
that the magnitude of the bias of the sample mean based on the rMAB is substantially
smaller than that of competing methods. In Chapter 3, we first explicitly derive the
exact bias formula for a family of estimators. It is shown that the bias term depends
on the average number of the times that a particular arm is pulled and the covariance
between the estimator and this number. To get a data-driven version method, we
introduce the RBA, a Resampling-based Bias Adjustment method, to calculate this
bias term. It is numerically shown that the RBA performs better than its competitors.
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