In this paper, we investigate score function-based tests to check the significance of an ultrahigh-dimensional sub-vector of the model coefficients when the nuisance parameter vector is also ultrahigh-dimensional in linear models. We first reanalyze and extend a recently proposed score function-based test to derive, under weaker conditions, its limiting distributions under the null and local alternative hypotheses. As it may fail to work when the correlation between testing covariates and nuisance covariates is high, we propose an orthogonalized score function-based test with two merits: debiasing to make the non-degenerate error term degenerate and reducing the asymptotic variance to enhance power performance. Simulations evaluate the finite-sample performances of the proposed tests, and a real data analysis illustrates its application.

翻译：本文研究基于得分函数的检验方法，用于检验线性模型中当干扰参数向量同样为超高维时，模型系数中某个超高维子向量的显著性。我们首先重新分析并扩展了近期提出的一种基于得分函数的检验方法，在更弱的条件下推导了其在原假设与局部备择假设下的极限分布。由于当检验协变量与干扰协变量间相关性较高时，该方法可能失效，我们提出了一种正交化的基于得分函数的检验方法，该方法具有两大优势：通过去偏使非退化误差项退化为退化项，并通过降低渐近方差以提升检验功效。仿真实验评估了所提检验方法的有限样本性能，并通过实际数据分析展示了其应用价值。