Modern data applications often lead the problem to a high-dimensional regime, where the data dimension can be larger than the sample size. This phenomenon brings challenges to the classical statistical testing procedures, even in many basic settings. In this work, we consider the problem of hypothesis testing in high-dimensional single-index models. First, we study the feasibility of applying the classical F-test to a single-index model when the dimension of covariate vector and sample size are of the same order, and derive its asymptotic null distribution and asymptotic local power function. For the ultrahigh-dimensional single-index model, we construct F-statistics based on lower-dimensional random projections of the data, and establish the asymptotic null distribution and the asymptotic local power function of the proposed test statistics for the hypothesis testing of global and partial parameters. The new proposed test possesses the advantages of having a simple structure as well as being easy to compute. We compare the proposed test with other high-dimensional tests and provide sufficient conditions under which the proposed tests are more efficient. We conduct simulation studies to evaluate the finite-sample performances of the proposed tests and demonstrate that it has higher power than some existing methods in the models we consider. The application of real high-dimensional gene expression data is also provided to illustrate the effectiveness of the method.
刘常钰目前在香港中文大学统计系担任博士后研究员。在此之前，她曾在香港理工大学担任博士后研究员。她于2021年在香港理工大学获得统计学博士学位，2017年在武汉大学获得基础数学学士学位。她的主要研究兴趣包括机器学习、图模型、生存分析和高维统计。她的研究成果已发表在《Journal of the American Statistical Association》和《Statistica Sinica》等期刊上