Tests and variables selection on regression analysis for massive datasets

According to Lindley's paradox, most point null hypotheses will be rejected when the sample size is too large. In this paper, a two-stage block testing procedure is proposed for massive data regression analysis. New variables selection criteria incorporating with classical stepwise procedure are also developed to select significant explanatory variables. Our approach is not only simple in computation for massive data but also confirmed by the simulation study that our approach is more accurate in the sense of achieving the nominal significance level for huge data sets. A real example with moderate sample size verifies that the proposed procedure is accurate compared with the classical method, and a huge real data set is also demonstrated to select appropriate regressors.