# Statistical inference on restricted partially linear additive errors-in-variables models

## Author Info

• Chuanhua Wei

()

• Qihua Wang
Registered author(s):

## 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. Copyright Sociedad de Estadística e Investigación Operativa 2012

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File URL: http://hdl.handle.net/10.1007/s11749-011-0279-6

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## Bibliographic Info

Article provided by Springer in its journal TEST.

Volume (Year): 21 (2012)
Issue (Month): 4 (December)
Pages: 757-774

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## References

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1. Manzan, Sebastiano & Zerom, Dawit, 2005. "Kernel estimation of a partially linear additive model," Statistics & Probability Letters, Elsevier, vol. 72(4), pages 313-322, May.
2. Wang, Qihua, 1999. "Estimation of Partial Linear Error-in-Variables Models with Validation Data," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 30-64, April.
3. You, Jinhong & Chen, Gemai, 2006. "Estimation of a semiparametric varying-coefficient partially linear errors-in-variables model," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 324-341, February.
4. Opsomer, Jean D., 2000. "Asymptotic Properties of Backfitting Estimators," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 166-179, May.
5. Qihua Wang, 2002. "Empirical likelihood-based inference in linear errors-in-covariables models with validation data," Biometrika, Biometrika Trust, vol. 89(2), pages 345-358, June.
6. Shalabh & Garg, Gaurav & Misra, Neeraj, 2007. "Restricted regression estimation in measurement error models," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 1149-1166, October.
7. Przystalski, Marcin & Krajewski, Pawel, 2007. "Constrained estimators of treatment parameters in semiparametric models," Statistics & Probability Letters, Elsevier, vol. 77(9), pages 914-919, May.
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