Statistical inference using regularized M-estimation in the reproducing kernel Hilbert space for handling missing data
Statistical inference using regularized M-estimation in the reproducing kernel Hilbert space for handling missing data
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DOI：
10.1007/s10463-023-00872-8
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发表时间：
2021-07
影响因子：
1
通讯作者：
Hengfang Wang;Jae Kwang Kim
中科院分区：
文献类型：
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作者：
Hengfang Wang;Jae Kwang Kim
插补是处理缺失数据的常用技术。在再生核Hilbert空间中，我们使用正则化M-估计技术解决了非参数插补问题。具体来说，我们首先使用核岭回归开发插补处理项目无应答。虽然这种非参数方法是潜在的有前途的插补，其统计特性没有在文献中进行研究。在调整参数的阶数一定的条件下，我们首先建立了核岭回归插补估计的根相合性，并证明了它达到了半参数渐近方差的下界。利用投影估计量的线性表达式，得到了一个基于再生核Hilbert空间的非参数倾向分数估计量。我们证明了由此得到的倾向得分估计渐近等价于核岭回归插补估计。有限的模拟研究的结果也证实了我们的理论。该方法被应用于分析空气污染的测量数据在北京，中国。
Imputation is a popular technique for handling missing data. We address a nonparametric imputation using the regularized M-estimation techniques in the reproducing kernel Hilbert space. Specifically, we first use kernel ridge regression to develop imputation for handling item nonresponse. Although this nonparametric approach is potentially promising for imputation, its statistical properties are not investigated in the literature. Under some conditions on the order of the tuning parameter, we first establish the root-nconsistency of the kernel ridge regression imputation estimator and show that it achieves the lower bound of the semiparametric asymptotic variance. A nonparametric propensity score estimator using the reproducing kernel Hilbert space is also developed by the linear expression of the projection estimator. We show that the resulting propensity score estimator is asymptotically equivalent to the kernel ridge regression imputation estimator. Results from a limited simulation study are also presented to confirm our theory. The proposed method is applied to analyze air pollution data measured in Beijing, China.