Department of Mathematics
Estimation of a groupwise additive multiple-index model and its applications
In this paper, we propose a simple linear least squares framework to deal with estimation and selection for a groupwise additive multiple-index model, of which the partially linear single-index model is a special case, and in which each component function has a single-index structure. We show that, somewhat unexpectedly, all index vectors can be recovered through a single least squares coefficient vector. As a direct application, for partially linear single-index models we develop a new two-stage estimation procedure that is iterative-free and easily implemented. This estimation approach can also be applied to develop, for the semi-parametric model under study, a penalized least squares estimation and establish its asymptotic behavior in sparse and high-dimensional settings without any nonparametric treatment. A simulation study and a data analysis are presented.
High dimensionality, Index estimation, Least squares, Multipleindex models, Variable selection
Source Publication Title
Academia Sinica, Institute of Statistical Science
Link to Publisher's Edition
Wang, T., Zhang, J., Liang, H., & Zhu, L. (2015). Estimation of a groupwise additive multiple-index model and its applications. Statistica Sinica, 25 (2), 551-566. https://doi.org/10.5705/ss.2013.175