Abstract
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.
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Acknowledgments
The authors thank the editor, the associate editor and two referees for their constructive comments and suggestions which led a substantial improvement of an early manuscript. The research described here was supported by a grant from the University Grants Council of Hong Kong, Hong Kong and National Natural Science Foundation of China (No. 11071253).
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Guo, X., Xu, W. & Zhu, L. Model checking for parametric regressions with response missing at random. Ann Inst Stat Math 67, 229–259 (2015). https://doi.org/10.1007/s10463-014-0451-3
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DOI: https://doi.org/10.1007/s10463-014-0451-3