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Estimation and hypothesis test for single-index multiplicative models

Author

Listed:
  • Jun Zhang

    (Shenzhen University)

  • Junpeng Zhu

    (Shenzhen University)

  • Zhenghui Feng

    (Xiamen University)

Abstract

Estimation and hypothesis tests for 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. For the hypothesis testing of parametric components, a Wald-type test statistic is proposed. The asymptotic properties of the estimators and test statistics are established, and a smoothly clipped absolute deviation penalty is employed to select the relevant variables. The resulting penalized estimators are shown to be asymptotically normal and have the oracle property. A score-type test statistic is then proposed for checking the validity of single-index multiplicative models. The quadratic form of the scaled test statistic has an asymptotic chi-squared distribution under the null hypothesis and follows a noncentral chi-squared distribution under local alternatives, converging to the null hypothesis at a parametric convergence rate. Simulation studies demonstrate the performance of the proposed procedure and a real example is analyzed to illustrate its practical usage.

Suggested Citation

  • Jun Zhang & Junpeng Zhu & Zhenghui Feng, 2019. "Estimation and hypothesis test for single-index multiplicative models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 242-268, March.
    • Handle: RePEc:spr:testjl:v:28:y:2019:i:1:d:10.1007_s11749-018-0586-2
    DOI: 10.1007/s11749-018-0586-2
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    References listed on IDEAS

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    Cited by:

    1. Jun Zhang & Bingqing Lin & Yiping Yang, 2022. "Maximum nonparametric kernel likelihood estimation for multiplicative linear regression models," Statistical Papers, Springer, vol. 63(3), pages 885-918, June.
    2. Jun Zhang, 2021. "Model checking for multiplicative linear regression models with mixed estimators," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(3), pages 364-403, August.
    3. Yinjun Chen & Hao Ming & Hu Yang, 2024. "Efficient variable selection for high-dimensional multiplicative models: a novel LPRE-based approach," Statistical Papers, Springer, vol. 65(6), pages 3713-3737, August.

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