This paper studies model checking for general parametric regression models with no dimension reduction structures 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：本文研究无降维结构高维预测向量下一般参数回归模型的模型检验问题。以现有检验为初始检验，结合样本拆分技术与条件学生化方法构建了条件学生化检验（COST）。与现有检验不同，无论初始检验基于全局或局部平滑，无论预测向量维度和参数数量固定还是随样本量发散至无穷，所提检验在原假设下均具有正态弱极限。进一步地，该检验能以假设检验中最优收敛速度检测与原假设相异的局部备择假设。本文还讨论了功率性能的最优样本拆分策略。数值研究揭示了其在有限样本情形下的优劣特性。作为一种通用方法论，该检验可推广至其他检验问题。