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Estimation in Partially Linear Single-Index Models with Missing Covariates |
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| Authors: | X. H. Liu Z. Z. Wang X. M. Hu |
| Affiliation: | 1. School of Mathematics Science and Computing Technology , Central South University , Hunuan , China;2. School of Statistics , Jiangxi University of Finance and Economics , Jiangxi , China csuliuxh912@gmail.com;4. School of Mathematics Science and Computing Technology , Central South University , Hunuan , China;5. Mathematics and Statistics College , Chongqing Technology and Business University , Chongqing , China;6. Academy of Mathematics and Systems Science , Chinese Academy of Sciences , Beijing , China |
| Abstract: | In this article, we consider a partially linear single-index model Y = g(Z τθ0) + X τβ0 + ? when the covariate X may be missing at random. We propose weighted estimators for the unknown parametric and nonparametric part by applying weighted estimating equations. We establish normality of the estimators of the parameters and asymptotic expansion for the estimator of the nonparametric part when the selection probabilities are unknown. Simulation studies are also conducted to illustrate the finite sample properties of these estimators. |
| Keywords: | Local linear regression Missing at random Partially linear single-index model Weighted estimating equations |