Department of Mathematics
In this paper, we propose simultaneous confidence bands for the nonparametric link function in single-index models in the presence of a nuisance index parameter. We establish the asymptotic properties for the link function and its derivative that allow simultaneous confidence bands for various inference tasks. In addition, we propose an adaptive Neyman test statistic for testing the linearity of the link function. We then conduct simulation studies to evaluate the performance of the proposed method, and apply them to two data sets for illustration.
Adaptive Neyman test, Difference-based estimator, Local linear smoother, Residual variance, Simultaneous confidence band, Single-index model
Source Publication Title
Academia Sinica, Institute of Statistical Science
Gaorong Li’s research was supported by the NSFC (11101014, 11201306), the Natural Science Foundation of Beijing (1142002), the Science and Technology Project of Beijing Municipal Education Commission (KM201410005010), the Specialized Research Fund for the Doctoral Program of Higher Education of China (20101103120016), PHR(IHLB, PHR20110822) and Program for JingHua Talents in Beijing University of Technology. Heng Peng’s research was supported by CERG grants from the Hong Kong Research Grants Council (HKBU 201610, HKBU 201809 and HKBU 202012), FRG grants from Hong Kong Baptist University (FRG2/11-12/130 and FRG2/12-13/077, and a grant from the NSFC (11271094). Tiejun Tong’s research was supported by Hong Kong RGC grant HKBU 202711.
Link to Publisher's Edition
Li, G., Peng, H., Dong, K., & Tong, T. (2014). Simultaneous confidence bands and hypothesis testing for single-index models. Statistica Sinica, 24 (2), 937-955. https://doi.org/10.5705/ss.2012.127