Fine-tuned Parallel Piecewise Sequential Confidence Region and Point Estimation Strategies for the Regression Parameters in a Linear Model: Big Data Context

Abstract

We introduced in our previous paper, fine-tuned parallel piecewise sequential sampling strategies for estimating the mean of a normal population. In this paper, we continue our explorations of sequential experimental designs for statistical inference in the context of big data. We develop fine-tuned parallel piecewise sequential methodologies for estimating the regression parameters in a linear model. Our proposed approaches achieve asymptotic unbiasedness of the stopping variable estimating the optimal fixed-sample size in addition to the operational efficiency with substantial time-savings when it comes to big data as a result of the parallel processing. We present a number of interesting illustrations of the theories and methodologies based on large-scale data analyses from simulated data as well as real data from a health study.

AMS Subject Classification: 62L1O, 62L05, 62L12, 62J05

Keywords

Asymptotic second-order efficiency big data data analysis fine-tuning fixed-size confidence region linear regression minimum risk point estimation parallel piecewise sequential sampling sequential sampling simulations stopping rule

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