Optimal Decorrelated Score Subsampling for High-Dimensional Generalized Linear Models Under Measurement Constraints
针对响应变量难以获取的高维广义线性模型，提出一种无需响应值的去相关得分子抽样方法，用于估计低维参数并进行统计推断，基于A和L最优准则设计最优抽样概率，并通过模拟和实际数据验证效果。
When responses of massive data are hard to obtain due to some reasons such as privacy and security, high cost and administrative management, response-free subsampling is considered. In this article, we propose a response-free decorrelated score subsampling approach to estimate and make statistical inference for a preconceived low-dimensional parameter in high-dimensional generalized linear models. The unconditional consistency and asymptotic normality of the resulting weighted subsample estimator are established using martingale techniques since the subsamples are no longer independent. The optimal response-free subsampling probabilities are derived based on A- and L-optimality criteria. Based on the optimal subsample, we further propose a more efficient and stable unweighted decorrelated score subsample estimator. The satisfactory performance of our proposed subsample estimators are demonstrated by simulation results and two real data applications. Supplementary materials for this article are available online.