Testing generalized linear models with high-dimensional nuisance parameters
提出一种计算高效的检验方法，用于广义线性模型中高维子系数的显著性检验，无需依赖计算昂贵的自助法，适用于稀疏或密集参数场景，并在中国饥荒样本数据中验证了基因-环境交互作用检验的性能。
Generalized linear models often have a high-dimensional nuisance parameters, as seen in applications such as testing gene-environment interactions or gene-gene interactions. In these scenarios, it is essential to test the significance of a high-dimensional sub-vector of the model's coefficients. Although some existing methods can tackle this problem, they often rely on the bootstrap to approximate the asymptotic distribution of the test statistic, and thus are computationally expensive. Here, we propose a computationally efficient test with a closed-form limiting distribution, which allows the parameter being tested to be either sparse or dense. We show that under certain regularity conditions, the type I error of the proposed method is asymptotically correct, and we establish its power under high-dimensional alternatives. Extensive simulations demonstrate the good performance of the proposed test and its robustness when certain sparsity assumptions are violated. We also apply the proposed method to Chinese famine sample data in order to show its performance when testing the significance of gene-environment interactions.