This paper studies model checking for general parametric regression models with no dimension reduction structure on the high-dimensional vector of predictors. Using existing test as an initial test, this paper combines the sample-splitting technique and conditional studentization approach to construct a COnditionally Studentized Test(COST). Unlike existing tests, whether the initial test is global or local smoothing-based, and whether the dimension of the predictor vector and the number of parameters are fixed, or diverge at a certain rate as the sample size goes to infinity, the proposed test always has a normal weak limit under the null hypothesis. Further, the test can detect the local alternatives distinct from the null hypothesis at the fastest possible rate of convergence in hypothesis testing. We also discuss the optimal sample splitting in power performance. The numerical studies offer information on its merits and limitations in finite sample cases. As a generic methodology, it could be applied to other testing problems.

翻译：本文研究了一类预测变量为高维向量且无降维结构的广义参数回归模型的模型检验问题。以现有检验作为初始检验，结合样本分割技术与条件学生化方法，构建了一种条件学生化检验（COST）。与现有检验不同——无论初始检验基于全局或局部平滑处理，也无论预测变量维度和参数个数是固定值还是随样本量增大以特定速率发散——本检验在原假设下始终具有正态弱极限。此外，该检验能以假设检验中最优收敛速度检测到与原假设不同的局部备择假设。本文还讨论了最优样本分割对检验功效的影响。数值研究揭示了该方法在有限样本情形下的优势与局限。作为一种通用方法，该检验可推广至其他检验问题。