Kernel machine in semiparametric regression with nonignorable missing responses

Pub Date : 2024-07-26 DOI:10.1007/s42952-024-00279-y
Zhenzhen Fu, Ke Yang, Yaohua Rong, Yu Shu
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Abstract

Missing data is prevalent in many fields. Among all missing mechanisms, nonignorable missing data is more challenging for model identification. In this paper, we propose a semiparametric regression model estimation method with nonignorable missing responses. To be specific, we first construct a parametric model for the propensity score and apply the generalized method of moments to obtain the estimated propensity score. For nonignorable missing responses, based on the inverse probability weighting approach, we propose the penalized garrotized kernel machine method to flexibly depict the complex nonlinear relationships between the response and the predictors, allow for interactions between the predictors, and eliminate the redundant variables automatically. The cyclical coordinate descent algorithm is provided to solve the corresponding optimization problems. Numerical results and real data analysis indicate that our proposed method achieves better prediction performance compared with the competing ones.

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具有不可忽略的缺失响应的半参数回归中的核机器
缺失数据在许多领域都很普遍。在所有缺失机制中,不可忽略的缺失数据对模型识别来说更具挑战性。本文提出了一种具有不可忽略的缺失响应的半参数回归模型估计方法。具体来说,我们首先为倾向得分构建一个参数模型,然后应用广义矩方法得到估计的倾向得分。对于不可忽略的缺失反应,我们在反概率加权法的基础上,提出了惩罚性加权核机器方法,以灵活地描述反应与预测因子之间复杂的非线性关系,允许预测因子之间的交互作用,并自动消除冗余变量。此外,还提供了循环坐标下降算法来解决相应的优化问题。数值结果和实际数据分析表明,与其他竞争方法相比,我们提出的方法具有更好的预测性能。
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