Group inference of high-dimensional single-index models

Abstract

For the supervised and semi-supervised settings, a group inference method is proposed for regression parameters in high-dimensional semi-parametric single-index models with an unknown random link function. The inference procedure is based on least squares, which can be extended to other general convex loss functions. The proposed test statistics are weighted quadratic forms of the regression parameter estimates, in which the weight could be a non-random matrix or the sample covariance matrix of the covariates. The proposed method could detect dense but weak signals and deal with high correlation of covariates inside the group. A ‘contaminated test statistic’ is established in the semi-supervised regime to decrease the variance. The asymptotic properties of the resulting estimators are established. The finite-sample behaviour of the proposed method is evaluated through extensive simulation studies. Applications to two genomic datasets are provided.

Keywords:

• Group inference
• high dimension
• hypothesis testing
• single-index models
• semi-supervised learning

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Dongxiao Han is partly supported by the National Natural Science Foundation of China (No. 12101330, No. 12231011), Shenzhen Wukong Investment Management Co. Ltd, the Fundamental Research Funds for the Central Universities, Nankai University (No. 63241563), and Tianjin Municipal Natural Science Foundation (No. 23JCYBJC01270). Miao Han is partly supported in part by the National Natural Science Foundation of China (No. 11601307), Shanghai Pujiang Program (No. 2020PJC053) and IRTSHUFE from the Shanghai University of Finance and Economics. Meiling Hao is partly supported by the Fundamental Research Funds for the Central Universities in UIBE (CXTD14-05) and the National Natural Science Foundation of China (No. 12371264, No. 12171329). Liuquan Sun is partially supported by the National Natural Science Foundation of China (No. 12171463).