An efficient estimation for the parameter in additive partially linear models with missing covariates
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Online ISSN 2005-2863 Print ISSN 1226-3192
RESEARCH ARTICLE
An efficient estimation for the parameter in additive partially linear models with missing covariates Xiuli Wang1 · Yunquan Song2 · Shuxia Zhang1,3 Received: 7 April 2019 / Accepted: 23 October 2019 © Korean Statistical Society 2020
Abstract In this paper, we study the weighted quantile average estimation technique for the parameter in additive partially linear models with missing covariates, which is proved to be an efficient method. The proposed method is based on optimally combining information over different quantiles via multiple quantile regression. We establish asymptotic normality of the weighted quantile average estimators when the selection probability is known, estimated using the non-parametrical method and parametrical method, respectively. Moreover, we compute optimal weights by minimizing asymptotic variance and then obtain the corresponding optimal weighted quantile average estimators. To examine the finite performance of our proposed method, we use the numerical simulations and apply to model time sober for the patients from a rehabilitation center. Simulation results and data analysis further verify that the proposed method is an efficient and safe alternative to both the WCQR method and WLS method. Keywords Optimal weighted quantile estimation · Additive partially linear models · Missing covariates · Inverse probability weighted · B-spline
1 Introduction Classical statistical methods and the related theories are based on fully observed data, but in practical applications such as surveys, medical studies, psychological sciences and other scientific experiments, the respondents are reluctant to provide the
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Xiuli Wang [email protected] Yunquan Song [email protected]
1
School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, People’s Republic of China
2
College of Science, China University of Petroleum, Qingdao 266580, People’s Republic of China
3
Middle school attached to Shandong University, Jinan 250100, People’s Republic of China
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Journal of the Korean Statistical Society
information that the researchers need. In addition, the process of research is full of uncontrollable factors, so we cannot obtain all the data we want and often encounter the case of missing data. In the case of missing data, the standard statistical method cannot be directly applied to the corresponding statistical analysis. Many statisticians have been working on how to use the observed data to obtain effective statistical inference. So far there are several different kinds of methods such as complete-case (CC) analysis method, imputation method and inverse probability weighted method (IPW) and likelihood based method to handle the missing data problem. The complete-case (CC) method excludes subjects with missing data and only uses the fully observed data to infer. This method will lose the estimation efficiency due to the disregard of the information from the missing values, and may result in biased results if the
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