Unweighted Estimation Based on Optimal Sample Under Measurement Constraints

• Activity Number: 15 - Subsampling: Basic Tool That Facilitates the Identification of Statistical Relationships in Big Data
• Type: Topic Contributed
• Date/Time: Sunday, August 7, 2022 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Jing Wang*
• Companies: University of Connecticut
• Keywords: Massive data; Generalized linear models; Martingale central limit theorem

Abstract

To tackle massive data, subsampling is a practical approach to sift more informative data points. However, when responses are expensive to measure, developing efficient subsampling schemes is challenging, and the 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 on 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 existing subsampling literature. Both asymptotic results and numerical results show that the unweighted estimator is more efficient in parameter estimation.