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Testing the significance of index parameters in varying-coefficient single-index models

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  • Wong, Heung
  • Zhang, Riquan
  • Leung, Bartholomew
  • Huang, Zhensheng

Abstract

The varying-coefficient single-index models (VCSIMs) form a class of very flexible and general dimension reduction models, which contain many important regression models such as partially linear models, pure single-index models, partially linear single-index models, varying-coefficient models and so on as special examples. However, the testing problems of the index parameter of the VCSIM have not been very well developed, due partially to the complexity of the models. To this end, based on the estimators obtained by the local linear method and the backfitting technique, we propose the generalized F-type test method to deal with the testing problems of the index parameters of the VCSIM. It is shown that under the null hypothesis the proposed test statistic follows asymptotically a χ2-distribution with the scale constant and the degrees of freedom being independent of the nuisance parameters or functions, which is called the Wilks phenomenon. Simulated data and real data examples are used to illustrate our proposed methodology.

Suggested Citation

  • Wong, Heung & Zhang, Riquan & Leung, Bartholomew & Huang, Zhensheng, 2013. "Testing the significance of index parameters in varying-coefficient single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 297-308.
    • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:297-308
    DOI: 10.1016/j.csda.2012.07.002
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    References listed on IDEAS

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    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, June.
    2. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
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    4. Ip, Wai-Cheung & Wong, Heung & Zhang, Riquan, 2007. "Generalized likelihood ratio test for varying-coefficient models with different smoothing variables," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4543-4561, May.
    5. Wong, Heung & Ip, Wai-cheung & Zhang, Riquan, 2008. "Varying-coefficient single-index model," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1458-1476, January.
    6. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
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