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Inverse probability weighted estimators for single-index models with missing covariates

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  • Tingting Li
  • Hu Yang

Abstract

In 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.

Suggested Citation

  • Tingting Li & Hu Yang, 2016. "Inverse probability weighted estimators for single-index models with missing covariates," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(5), pages 1199-1214, March.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:5:p:1199-1214
    DOI: 10.1080/03610926.2012.705208
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    Cited by:

    1. Huilan Liu & Hu Yang & Changgen Peng, 2019. "Weighted composite quantile regression for single index model with missing covariates at random," Computational Statistics, Springer, vol. 34(4), pages 1711-1740, December.
    2. Takuma Yoshida, 2019. "Two stage smoothing in additive models with missing covariates," Statistical Papers, Springer, vol. 60(6), pages 1803-1826, December.

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