Abstract
As a useful extension of partially linear models and additive models, partially linear additive model has been paid considerable attention in recent years. This paper considers statistical inference for the semiparametric model when the covariates in the linear part are measured with additive error. To test hypothesis on the parametric component, we propose a novel test statistic based on the difference between the corrected residual sums of squares under the null and alternative hypotheses, and show that its limiting distribution is that of a weighted sum of independent standard \(\chi_{1}^{2}\). We also develop an adjusted test statistic, which has an asymptotically standard chi-squared distribution. Some simulation studies are conducted to illustrate our approaches.
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Acknowledgements
The authors would like to thank the Editor, an Associate Editor and two referees for their truly helpful comments and suggestions which led to a much improved presentation. Chuanhua Wei’s research was supported by The Philosophy and Social Science Foundation of China (No. 07CTJ003), and “211” Project Foundation of Minzu University of China (No. 021211030312). Qihua Wang’s research was supported by the National Science Fund for Distinguished Young Scholars in China (10725106), the National Natural Science Foundation of China (10671198), the National Science Fund for Creative Research Groups in China, a grant from the Key Lab of Random Complex Structure and Data Science, CAS and the Key grant from Yunnan Province (2010CC003).
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Wei, C., Wang, Q. Statistical inference on restricted partially linear additive errors-in-variables models. TEST 21, 757–774 (2012). https://doi.org/10.1007/s11749-011-0279-6
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DOI: https://doi.org/10.1007/s11749-011-0279-6
Keywords
- Errors-in-variables
- Partially linear additive model
- Corrected-profile least-squares approach
- Restricted estimator