Inverse probability weighted estimators for single-index models with missing covariates |
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Authors: | Tingting Li Hu Yang |
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Affiliation: | 1. School of Mathematics and Statistics, Southwest University, Chongqing, China;2. College of Mathematics and Statistics, Chongqing University, Chongqing, Chinatinalee@swu.edu.cn;4. College of Mathematics and Statistics, Chongqing University, Chongqing, China |
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Abstract: | AbstractIn this article, we consider the inverse probability weighted estimators for a single-index model with missing covariates when the selection probabilities are known or unknown. It is shown that the estimator for the index parameter by using estimated selection probabilities has a smaller asymptotic variance than that with true selection probabilities, thus is more efficient. Therefore, the important Horvitz-Thompson property is verified for the index parameter in single index model. However, this difference disappears for the estimators of the link function. Some numerical examples and a real data application are also conducted to illustrate the performances of the estimators. |
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Keywords: | Single-index models Missing covariates at random Horvitz-Thompson property. |
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