Estimation and testing of expectile regression with efficient subsampling for massive data

Subsampling strategy plays a crucial role in statistical inference for massive data owing to its computing and storage superiority. The parameter estimation and hypothesis testing of expectile regression for massive data is of concern. This paper offers an alternative to the traditional asymmetric least square (ALS) estimator via smooth approximation of loss function. Then, an efficient subsampling algorithm based on Newton’s iteration is proposed. We prove consistency and asymptotic normality and provide the optimal subsampling probability and the proper order of smoothing parameter. We also apply the subsampling strategy for hypothesis testing, where the proposed test statistics have bigger power, compared with the test statistic based on the simple random subsampling. Simulation and two real data examples demonstrate the effectiveness of the proposed subsampling estimation and testing methods.