Sampling Importance Resampling Algorithm with Nonignorable Missing Response Variable Based on Smoothed Quantile Regression

Jingxuan Guo, Fuguo Liu, Wolfgang Karl Härdle, Xueliang Zhang, Kai Wang, Ting Zeng, Liping Yang and Maozai Tian ()
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Jingxuan Guo: School of Statistics and Data Science, Beijing Wuzi University, Beijing 101149, China
Fuguo Liu: School of Statistics and Data Science, Xinjiang University of Finance and Economics, Urumqi 830012, China
Wolfgang Karl Härdle: Department of Information Management and Finance, National Yang Ming Chiao Tung University, Taiwan 30010, China
Xueliang Zhang: Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China
Kai Wang: Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China
Ting Zeng: Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China
Liping Yang: Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China
Maozai Tian: Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China

Mathematics, 2023, vol. 11, issue 24, 1-30

Abstract: The presence of nonignorable missing response variables often leads to complex conditional distribution patterns that cannot be effectively captured through mean regression. In contrast, quantile regression offers valuable insights into the conditional distribution. Consequently, this article places emphasis on the quantile regression approach to address nonrandom missing data. Taking inspiration from fractional imputation, this paper proposes a novel smoothed quantile regression estimation equation based on a sampling importance resampling (SIR) algorithm instead of nonparametric kernel regression methods. Additionally, we present an augmented inverse probability weighting (AIPW) smoothed quantile regression estimation equation to reduce the influence of potential misspecification in a working model. The consistency and asymptotic normality of the empirical likelihood estimators corresponding to the above estimating equations are proven under the assumption of a correctly specified parameter working model. Furthermore, we demonstrate that the AIPW estimation equation converges to an IPW estimation equation when a parameter working model is misspecified, thus illustrating the robustness of the AIPW estimation approach. Through numerical simulations, we examine the finite sample properties of the proposed method when the working models are both correctly specified and misspecified. Furthermore, we apply the proposed method to analyze HIV—CD4 data, thereby exploring variations in treatment effects and the influence of other covariates across different quantiles.

Keywords: empirical likelihood; nonignorable missing; quantile regression; sampling importance resampling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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