Model checking for parametric regressions with response missing at random

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• 作者：Xu Guo (1) (2)
  Wangli Xu (3)
  Lixing Zhu (4)
  
  1. Department of Mathematics ; Hong Kong Baptist University ; Fong Shu-Chuen Library 1110 ; Kowloon Tong ; Hong Kong
  2. College of Economics and Management ; Nanjing University of Aeronautics and Astronautics ; 29 Jiangjun Avenue ; 210016 ; Nanjing ; China
  3. School of Statistics ; Center for Applied Statistics ; Renmin University of China ; Zhongguancun Street 59 ; 100872聽 ; Beijing ; China
  4. Department of Mathematics ; Hong Kong Baptist University ; Fong Shu Chuen Library 1208 Waterloo Road 224 ; Kowloon Tong ; Hong Kong
  
• 关键词：Inverse probability weight ; Response missing at random ; Model checking
• 刊名：Annals of the Institute of Statistical Mathematics
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：67
• 期：2
• 页码：229-259
• 全文大小：363 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics
  Statistics for Business, Economics, Mathematical Finance and Insurance
  
• 出版者：Springer Netherlands
• ISSN：1572-9052

文摘

This paper aims at investigating model checking for parametric models with response missing at random which is a more general missing mechanism than missing completely at random. Different from existing approaches, two tests have normal distributions as the limiting null distributions no matter whether the inverse probability weight is estimated parametrically or nonparametrically. Thus, \(p\) values can be easily determined. This observation shows that slow convergence rate of nonparametric estimation does not have significant effect on the asymptotic behaviors of the tests although it may have impact in finite sample scenarios. The tests can detect the alternatives distinct from the null hypothesis at a nonparametric rate which is an optimal rate for locally smoothing-based methods in this area. Simulation study is carried out to examine the performance of the tests. The tests are also applied to analyze a data set on monozygotic twins for illustration.