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Acta Mathematicae Applicatae Sinica, English Series 2012, Vol. 28 Issue (1) :99-110    DOI: 10.1007/s10255-012-0125-y
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Model Checking for a General Linear Model with Nonignorable Missing Covariates
Zhi-hua SUN1,2, Wai-Cheung IP3, Heung WONG3
1. School of Mathematical sciences, Graduate University of Chinese Academy of Sciences, Beijing 100049, China;
2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
3. Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China
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Abstract In this paper, we investigate the model checking problem for a general linear model with nonignorable missing covariates. We show that, without any parametric model assumption for the response probability, the least squares method yields consistent estimators for the linear model even if only the complete data are applied. This makes it feasible to propose two testing procedures for the corresponding model checking problem: a score type lack-of-fit test and a test based on the empirical process. The asymptotic properties of the test statistics are investigated. Both tests are shown to have asymptotic power 1 for local alternatives converging to the null at the rate n-r, 0 ≤ r < (1/2). Simulation results show that both tests perform satisfactorily.  
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Keywordsgeneral linear model   model checking   nonignorable missing covariates   sensitivity analysis     
Abstract: In this paper, we investigate the model checking problem for a general linear model with nonignorable missing covariates. We show that, without any parametric model assumption for the response probability, the least squares method yields consistent estimators for the linear model even if only the complete data are applied. This makes it feasible to propose two testing procedures for the corresponding model checking problem: a score type lack-of-fit test and a test based on the empirical process. The asymptotic properties of the test statistics are investigated. Both tests are shown to have asymptotic power 1 for local alternatives converging to the null at the rate n-r, 0 ≤ r < (1/2). Simulation results show that both tests perform satisfactorily.  
Keywordsgeneral linear model,   model checking,   nonignorable missing covariates,   sensitivity analysis     
Received: 2010-02-25;
Fund:

Zhihua Sun’research was supported by the National Natural Science Foundation of China (No. 10901162, 10926073), China Postdoctoral Science Foundation and the President Fund of GUCAS, the foundation of the Key Laboratory of Random Complex Structures and Data Science, CAS; Wai-Cheung IP and Heung Wong’s research was supported by a research grant from the Research Committee, The Hong Kong Polytechnic University.

Cite this article:   
.Model Checking for a General Linear Model with Nonignorable Missing Covariates[J]  Acta Mathematicae Applicatae Sinica, English Serie, 2012,V28(1): 99-110
URL:  
http://www.applmath.com.cn/jweb_yysxxb_en/EN/10.1007/s10255-012-0125-y      或     http://www.applmath.com.cn/jweb_yysxxb_en/EN/Y2012/V28/I1/99
 
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