Kavli Affiliate: Jing Wang
| First 5 Authors: Jing Wang, HaiYing Wang, Shifeng Xiong, ,
| Summary:
To tackle massive data, subsampling is a practical approach to select the
more informative data points. However, when responses are expensive to measure,
developing efficient subsampling schemes is challenging, and an optimal
sampling approach under measurement constraints was developed to meet this
challenge. This method uses the inverses of optimal sampling probabilities to
reweight the objective function, which assigns smaller weights to the more
important data points. Thus the estimation efficiency of the resulting
estimator can be improved. In this paper, we propose an unweighted estimating
procedure based on optimal subsamples to obtain a more efficient estimator. We
obtain the unconditional asymptotic distribution of the estimator via
martingale techniques without conditioning on the pilot estimate, which has
been less investigated in the existing subsampling literature. Both asymptotic
results and numerical results show that the unweighted estimator is more
efficient in parameter estimation.
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