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Profile Inferences on Restricted Additive Partially Linear EV Models

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  • Xiuli Wang

Abstract

We consider the testing problem for the parameter and restricted estimator for the nonparametric component in the additive partially linear errors‐in‐variables (EV) models under additional restricted condition. We propose a profile Lagrange multiplier test statistic based on modified profile least‐squares method and two‐stage restricted estimator for the nonparametric component. We derive two important results. One is that, without requiring the undersmoothing of the nonparametric components, the proposed test statistic is proved asymptotically to be a standard chi‐square distribution under the null hypothesis and a noncentral chi‐square distribution under the alternative hypothesis. These results are the same as the results derived by Wei and Wang (2012) for their adjusted test statistic. But our method does not need an adjustment and is easier to implement especially for the unknown covariance of measurement error. The other is that asymptotic distribution of proposed two‐stage restricted estimator of the nonparametric component is asymptotically normal and has an oracle property in the sense that, though the other component is unknown, the estimator performs well as if it was known. Some simulation studies are carried out to illustrate relevant performances with a finite sample. The asymptotic distribution of the restricted corrected‐profile least‐squares estimator, which has not been considered by Wei and Wang (2012), is also investigated.

Suggested Citation

  • Xiuli Wang, 2013. "Profile Inferences on Restricted Additive Partially Linear EV Models," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:594391
    DOI: 10.1155/2013/594391
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    References listed on IDEAS

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    1. Hua Liang & Sally W. Thurston & David Ruppert & Tatiyana Apanasovich & Russ Hauser, 2008. "Additive partial linear models with measurement errors," Biometrika, Biometrika Trust, vol. 95(3), pages 667-678.
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    4. 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.
    5. Chuanhua Wei & Qihua Wang, 2012. "Statistical inference on restricted partially linear additive errors-in-variables models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 757-774, December.
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