Dimension reduction in estimating equations with covariates missing at random

ABSTRACT

To estimate parameters defined by estimating equations with covariates missing at random, we consider three bias-corrected nonparametric approaches based on inverse probability weighting, regression and augmented inverse probability weighting. However, when the dimension of covariates is not low, the estimation efficiency will be affected due to the curse of dimensionality. To address this issue, we propose a two-stage estimation procedure by using the dimension-reduced kernel estimation in conjunction with bias-corrected estimating equations. We show that the resulting three estimators are asymptotically equivalent and achieve the desirable properties. The impact of dimension reduction in nonparametric estimation of parameters is also investigated. The finite-sample performance of the proposed estimators is studied through simulation, and an application to an automobile data set is also presented.

KEYWORDS:

• Consistency and asymptotic normality
• covariates missing
• dimension reduction
• kernel regression
• missing at random

AMS Subject Classifications:

• 62G05
• 62G08
• 62G20

Acknowledgments

We are grateful to the Editor, the Associate Editor, and two anonymous referees for their insightful comments and suggestions on this article, which have led to significant improvements.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11501208].