Optimal Subsampling Approaches for Large Sample Linear Regression

Understand

A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods.

• An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample from the original full sample and uses it as a surrogate for subsequent computation and estimation.
• In this paper, we study subsampling methods under two scenarios: approximating the full sample ordinary least-square (OLS) estimator and estimating the coefficients in linear regression.
• We present two algorithms, weighted estimation algorithm and unweighted estimation algorithm, and analyze asymptotic behaviors of their resulting subsample estimators under general conditions.