TY - JOUR
T1 - Multi-index regression models with missing covariates at random
AU - Guo, Xu
AU - Xu, Wangli
AU - ZHU, Lixing
N1 - Funding Information:
The research described here was supported by a grant from the University Grants Council of Hong Kong , Hong Kong, the distinguished Scientists program of King Abdulaziz University, Saudi Arabia when Lixing Zhu was a distinguished adjunct professor in the academic year of 2013–2014, Beijing Nova Program (2010B066), and National Nature Science Fund of China (No. 11071253 ). The authors thank the editor, the associate editor and two referees for their constructive comments and suggestions which led a substantial improvement of an early manuscript.
PY - 2014/1
Y1 - 2014/1
N2 - This paper considers estimation of the semiparametric multi-index model with missing covariates at random. A weighted estimating equation is suggested by invoking the inverse selection probability approach, and estimators of the indices are respectively defined when the selection probability is known in advance, is estimated parametrically and nonparametrically. The consistency is provided. For the single-index model, the large sample properties show that the estimators with both parametric and nonparametric plug-in estimations can play an important role to achieve smaller limiting variances than the estimator with the true selection probability. Simulation studies are carried out to assess the finite sample performance of the proposed estimators. The proposed methods are applied to an AIDS clinical trials dataset to examine which method could be more efficient. A horse colic dataset is also analyzed for illustration.
AB - This paper considers estimation of the semiparametric multi-index model with missing covariates at random. A weighted estimating equation is suggested by invoking the inverse selection probability approach, and estimators of the indices are respectively defined when the selection probability is known in advance, is estimated parametrically and nonparametrically. The consistency is provided. For the single-index model, the large sample properties show that the estimators with both parametric and nonparametric plug-in estimations can play an important role to achieve smaller limiting variances than the estimator with the true selection probability. Simulation studies are carried out to assess the finite sample performance of the proposed estimators. The proposed methods are applied to an AIDS clinical trials dataset to examine which method could be more efficient. A horse colic dataset is also analyzed for illustration.
KW - Covariates missing at random
KW - Inverse selection probability
KW - Multi-index model
KW - Single-index model
UR - http://www.scopus.com/inward/record.url?scp=84887218465&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2013.10.006
DO - 10.1016/j.jmva.2013.10.006
M3 - Article
AN - SCOPUS:84887218465
SN - 0047-259X
VL - 123
SP - 345
EP - 363
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
ER -
