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Simultaneous confidence bands for nonparametric regression with missing covariate data
Annals of the Institute of Statistical Mathematics ( IF 1 ) Pub Date : 2021-06-08 , DOI: 10.1007/s10463-021-00784-5
Li Cai , Lijie Gu , Qihua Wang , Suojin Wang

We consider a weighted local linear estimator based on the inverse selection probability for nonparametric regression with missing covariates at random. The asymptotic distribution of the maximal deviation between the estimator and the true regression function is derived and an asymptotically accurate simultaneous confidence band is constructed. The estimator for the regression function is shown to be oracally efficient in the sense that it is uniformly indistinguishable from that when the selection probabilities are known. Finite sample performance is examined via simulation studies which support our asymptotic theory. The proposed method is demonstrated via an analysis of a data set from the Canada 2010/2011 Youth Student Survey.



中文翻译:

具有缺失协变量数据的非参数回归的同时置信带

我们考虑一个基于逆选择概率的加权局部线性估计器,用于随机缺失协变量的非参数回归。推导出估计量与真实回归函数之间最大偏差的渐近分布,并构建渐近准确的同时置信带。回归函数的估计量被证明是口头上有效的,因为它与已知选择概率时的估计量完全无法区分。通过支持我们渐近理论的模拟研究来检查有限样本性能。所提出的方法通过对加拿大 2010/2011 年青年学生调查数据集的分析得到证明。

更新日期:2021-06-08
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