Statistical inference using regularized M-estimation in the reproducing kernel Hilbert space for handling missing data

IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY
Hengfang Wang, Jae Kwang Kim
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引用次数: 0

Abstract

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-n consistency 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.

Abstract Image

在再现核希尔伯特空间中使用正则化m估计处理缺失数据的统计推断
代入是处理缺失数据的常用技术。我们在再现核希尔伯特空间中使用正则化m估计技术来解决非参数输入问题。具体而言,我们首先使用核脊回归来开发处理项目无响应的输入。虽然这种非参数方法有可能用于估算,但其统计性质尚未在文献中进行研究。在一定的调优参数阶数条件下,我们首先建立了核脊回归估计量的根n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,提出了利用再现核希尔伯特空间的非参数倾向评分估计量。我们证明了所得的倾向分数估计量是渐近等价于核脊回归估计量。有限模拟研究的结果也证实了我们的理论。将该方法应用于北京地区的空气污染数据分析。
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来源期刊
CiteScore
2.00
自引率
0.00%
发文量
39
审稿时长
6-12 weeks
期刊介绍: Annals of the Institute of Statistical Mathematics (AISM) aims to provide a forum for open communication among statisticians, and to contribute to the advancement of statistics as a science to enable humans to handle information in order to cope with uncertainties. It publishes high-quality papers that shed new light on the theoretical, computational and/or methodological aspects of statistical science. Emphasis is placed on (a) development of new methodologies motivated by real data, (b) development of unifying theories, and (c) analysis and improvement of existing methodologies and theories.
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