We propose a new procedure to estimate the index parameter and link function of single-index models, where the response variable is subject to fixed censoring. Under some regularity conditions, we show that the estimated index parameter is root-n consistent and asymptotically normal, and the estimated nonparametric link function achieves the optimal convergence rate and is asymptotically normal. In addition, we propose a linearity testing method for the nonparametric link function. A simulation study shows that the proposed procedures perform well in finite-sample experiments. An application to an HIV data set is presented for illustrative purposes.
Huang, H., Li, Y., Liang, H., & Tang, Y. (2020). Estimation of Single-index Models with Fixed Censored Responses. Statistica Sinica. doi:10.5705/ss.202017.0451
The authors would like to thank the two reviewers, the associate editor, and the editor for their constructive comments and helpful suggestions. Liang's research was partially supported by National Science Foundation grant DMS-1418042 and DMS-1620898, National Natural Science Foundation of China grant, Award Number 11529101. Tang's research was partially supported by the OSR-2015-CRG4-2582 grant from KAUST, Shanghai Pujiang Program 18PJ1409800, and Key Laboratory for Applied Statistics of MOE, Northeast Normal University 130028849.