Collaborative Inference for Sparse High-Dimensional Models with Non-Shared Data
提出一种协作得分检验方法，用于非共享数据场景下高维线性假设检验，通过分解得分统计量并利用局部梯度信息，实现全局统计效率并放宽对数据源数量的限制。
In modern data analysis, an improvement in statistical efficiency is expected via effective collaboration among multiple data holders with non-shared data. In this article, we propose a collaborative score-type test (CST) for testing linear hypotheses, which accommodates potentially high-dimensional nuisance parameters and a diverging number of constraints and target parameters. Through a careful decomposition of the Kiefer-Bahadur representation for the traditional score statistic, we identify and approximate the key components using aggregated local gradient information from each data source. In addition, we employ a two-stage partial penalization strategy to shrink the approximation error and mitigate the bias from the high-dimensional nuisance parameters. Unlike existing methods, the CST procedure involves constrained optimization under non-shared and high-dimensional data settings, which requires novel theoretical developments. We derive the limiting distributions for the CST statistic under the null hypothesis and the local alternatives. Besides, the CST exhibits an oracle property and achieves the global statistical efficiency. Moreover, it relaxes the stringent restrictions on the number of data sources required in the current literature. Extensive numerical studies and a real-world example demonstrate the effectiveness and validity of our proposed method.