Optimal decorrelated score subsampling for generalized linear models with massive data

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外文摘要：In this paper,we consider the unified optimal subsampling estimation and inference on the low-dimensional parameter of main interest in the presence of the nuisance parameter for low/high-dimensional generalized linear models(GLMs)with massive data.We first present a general subsampling decorrelated score function to reduce the influence of the less accurate nuisance parameter estimation with the slow convergence rate.The consistency and asymptotic normality of the resultant subsample estimator from a general decorrelated score subsampling algorithm are established,and two optimal subsampling probabilities are derived under the A-and L-optimality criteria to downsize the data volume and reduce the computational burden.The proposed optimal subsampling probabilities provably improve the asymptotic efficiency of the subsampling schemes in the low-dimensional GLMs and perform better than the uniform subsampling scheme in the high-dimensional GLMs.A two-step algorithm is further proposed to implement,and the asymptotic properties of the corresponding estimators are also given.Simulations show satisfactory performance of the proposed estimators,and two applications to census income and Fashion-MNIST datasets also demonstrate its practical applicability.

外文关键词：

A-optimalitydecorrelated score subsamplinghigh-dimensional inferenceL-optimalitymassive data

作者：

Junzhuo Gao、Lei Wang、Heng Lian

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作者单位：

School of Statistics and Data Science & LPMC,Nankai University,Tianjin 300071,China

Department of Mathematics,City University of Hong Kong,Hong Kong,China

基金：

Fundamental Research Funds for the Central UniversitiesNational Natural Science Foundation of ChinaKey Laboratory for Medical Data Analysis and Statistical Research of Tianjin

项目编号：

12271272

出版年：

2024

DOI：

10.1007/s11425-022-2057-8

中国科学:数学(英文版)

中国科学院

中国科学:数学(英文版)

CSTPCD

影响因子：0.36

ISSN：1674-7283

年,卷(期)：2024.67(2)

参考文献量38