Poisson subsampling-based estimation for growing-dimensional expectile regression in massive data

As an effective tool for data analysis, expectile regression is widely used in the fields of statistics, econometrics and finance. However, most studies focus on the case where the sample size is not massive and the dimension is low or fixed. This paper studies the parameter estimation and inference for large-scale expectile regression when the number of parameters grows to infinity. Specifically, an inverse probability weighted asymmetric least squares estimator based on Poisson subsampling (ALS-P) is proposed. Theoretically, the convergence rate and asymptotic normality for ALS-P are established. Furthermore, the optimal subsampling probabilities based on the L-optimality criterion are derived. Finally, extensive simulations and two real-world datasets are conducted to illustrate the effectiveness of the proposed methods.