Abstract
We investigate semi-parametric small area inference in generalized semi-varying coefficient mixed effects models with application to longitudinal data. Combining the generalized profiled likelihood approaches for mixed effect models with kernel methods, we not only construct semi-parametric small area estimators, but also propose two test statistics for discriminating between a parametric mixed effects model and a generalized semi-varying coefficient mixed effects model. The critical values are estimated by a bootstrap procedure. The asymptotic theory for the methods is provided. Simulations exhibit the finite-sample performance for the proposed estimators and test statistics. These verify the feasibility and the excellent behavior of the methods for moderate sample sizes.
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Acknowledgements
The author would like to thank the anonymous referees and the Editor for useful comments which led to an improved version of the paper. Hu’s research was supported by the National Natural Science Foundation of China (No. 11101452), the Ministry of Education Humanity Social Science Research Project of China(No. 15YJC910002), the Natural Science Foundation of CQ CSTC (cstc.2015jcyjA00017, cstc2015jcyjA00009), the SCR of the Chongqing Municipal Education Commission (No. KJ1400613), the National Basic Research Program of China (973 Program, No. 2011CB808000) and the Program for University Innovation Team of Chongqing (CXTDX201601026), and Yang’s research was supported by the National Social Science Foundation of China (No. 13CTJ016).
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Hu, X., Yang, W. Semi-parametric small area inference in generalized semi-varying coefficient mixed effects models. Stat Papers 60, 1039–1058 (2019). https://doi.org/10.1007/s00362-016-0862-8
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DOI: https://doi.org/10.1007/s00362-016-0862-8
Keywords
- Semi-parametric inference
- Mixed effects models
- Bootstrap
- Generalized semi-varying coefficient mixed effects models
- Longitudinal data