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Statistical inference on parametric part for partially linear single-index model

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Abstract

Statistical inference on parametric part for the partially linear single-index model (PLSIM) is considered in this paper. A profile least-squares technique for estimating the parametric part is proposed and the asymptotic normality of the profile least-squares estimator is given. Based on the estimator, a generalized likelihood ratio (GLR) test is proposed to test whether parameters on linear part for the model is under a contain linear restricted condition. Under the null model, the proposed GLR statistic follows asymptotically the χ2-distribution with the scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Both simulated and real data examples are used to illustrate our proposed methods.

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Authors and Affiliations

  1. School of Finance and Statistics, East China Normal University, Shanghai, 200241, China

    RiQuan Zhang & ZhenSheng Huang

  2. Department of Mathematics, Shanxi Datong University, Datong, 037009, China

    RiQuan Zhang

Authors
  1. RiQuan Zhang
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  2. ZhenSheng Huang
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Corresponding author

Correspondence to RiQuan Zhang.

Additional information

This work was supported by National Natural Science Foundation of China (Grant No. 10871072), Natural Science Foundation of Shanxi Province of China (Grant No. 2007011014) and PhD Program Scholarship Fund of ECNU 2009

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Zhang, R., Huang, Z. Statistical inference on parametric part for partially linear single-index model. Sci. China Ser. A-Math. 52, 2227–2242 (2009). https://doi.org/10.1007/s11425-009-0079-6

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  • DOI: https://doi.org/10.1007/s11425-009-0079-6

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