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Estimation and hypothesis test for partial linear single-index multiplicative models

Author

Listed:
  • Jun Zhang

    (Shenzhen University)

  • Xia Cui

    (Guangzhou University)

  • Heng Peng

    (The Hong Kong Baptist University)

Abstract

Estimation and hypothesis test for partial linear single-index multiplicative models are considered in this paper. To estimate unknown single-index parameter, we propose a profile least product relative error estimator coupled with a leave-one-component-out method. To test a hypothesis on the parametric components, a Wald-type test statistic is proposed. We employ the smoothly clipped absolute deviation penalty to select relevant variables. To study model checking problem, we propose a variant of the integrated conditional moment test statistic by using linear projection weighting function, and we also suggest a bootstrap procedure for calculating critical values. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analyzed for illustration.

Suggested Citation

  • Jun Zhang & Xia Cui & Heng Peng, 2020. "Estimation and hypothesis test for partial linear single-index multiplicative models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 699-740, June.
    • Handle: RePEc:spr:aistmt:v:72:y:2020:i:3:d:10.1007_s10463-019-00706-6
    DOI: 10.1007/s10463-019-00706-6
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    References listed on IDEAS

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