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Estimation and hypothesis test for partial linear multiplicative models

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  • Zhang, Jun
  • Feng, Zhenghui
  • Peng, Heng

Abstract

Estimation and hypothesis tests for partial linear multiplicative models are considered in this paper. A profile least product relative error estimation method is proposed to estimate unknown parameters. We employ the smoothly clipped absolute deviation penalty to do variable selection. A Wald-type test statistic is proposed to test a hypothesis on parametric components. The asymptotic properties of the estimators and test statistics are established. We also suggest a score-type test statistic for checking the validity of partial linear multiplicative models. The quadratic form of the scaled test statistic has an asymptotic chi-squared distribution under the null hypothesis and follows a non-central chi-squared distribution under local alternatives, converging to the null hypothesis at a parametric convergence rate. We conduct simulation studies to demonstrate the performance of the proposed procedure and a real data is analyzed to illustrate its practical usage.

Suggested Citation

  • Zhang, Jun & Feng, Zhenghui & Peng, Heng, 2018. "Estimation and hypothesis test for partial linear multiplicative models," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 87-103.
    • Handle: RePEc:eee:csdana:v:128:y:2018:i:c:p:87-103
    DOI: 10.1016/j.csda.2018.06.017
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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.
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    3. Huilan Liu & Xiawei Zhang & Huaiqing Hu & Junjie Ma, 2024. "Analysis of the positive response data with the varying coefficient partially nonlinear multiplicative model," Statistical Papers, Springer, vol. 65(5), pages 3063-3092, July.
    4. Dong, Ruipeng & Li, Daoji & Zheng, Zemin, 2021. "Parallel integrative learning for large-scale multi-response regression with incomplete outcomes," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).

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