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Testing structural change in partially linear single-index models with error-prone linear covariates


  • Huang, Zhensheng
  • Pang, Zhen
  • Hu, Tao


Motivated by an analysis of a real data set from Duchenne Muscular Dystrophy (Andrews and Herzberg, 1985), we propose a new test of structural change for a class of partially linear single-index models with error-prone linear covariates. Based on the local linear estimation for the unknowns in these semiparametric models, we develop a new generalized F-test statistics for the nonparametric part in the partially linear single-index models with error-prone linear covariates. Asymptotic properties of the newly proposed test statistics are proved to follow asymptotically the chi-squared distribution. The new Wilks’ phenomenon is unveiled in a class of semiparametric measure error models. Simulations are conducted to examine the performance of our proposed method. The simulation results are consistent with our theoretical findings. Real data examples are used to illustrate the proposed methodology.

Suggested Citation

  • Huang, Zhensheng & Pang, Zhen & Hu, Tao, 2013. "Testing structural change in partially linear single-index models with error-prone linear covariates," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 121-133.
  • Handle: RePEc:eee:csdana:v:59:y:2013:i:c:p:121-133 DOI: 10.1016/j.csda.2012.10.002

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    References listed on IDEAS

    1. Lixing Zhu & Liugen Xue, 2006. "Empirical likelihood confidence regions in a partially linear single-index model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 549-570.
    2. Yanyuan Ma & Jeffrey D. Hart & Ryan Janicki & Raymond J. Carroll, 2011. "Local and omnibus goodness‐of‐fit tests in classical measurement error models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 81-98, January.
    3. 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.
    4. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    5. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    6. Wu, Tracy Z. & Yu, Keming & Yu, Yan, 2010. "Single-index quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1607-1621, August.
    7. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
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