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Maximum nonparametric kernel likelihood estimation for multiplicative linear regression models

Author

Listed:
  • Jun Zhang

    (Shenzhen University)

  • Bingqing Lin

    (Shenzhen University)

  • Yiping Yang

    (Chongqing Technology and Business University)

Abstract

We propose a kernel density based estimation for multiplicative linear regression models. The method proposed in this article makes use of kernel smoothing nonparametric techniques to estimate the unknown density function of model error. For the hypothesis testing of parametric components, restricted estimators under the null hypothesis and test statistics are proposed. The asymptotic properties for the estimators and test statistics are established. We illustrate our proposals through simulations and an analysis of the QSAR fish bioconcentration factor data set. Our analysis provides strong evidence that the proposed kernel density based estimator is superior than the least squares estimator and least product relative error estimator in the literature, particularly for multimodal or asymmetric or heavy-tailed distributions of the model error.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:3:d:10.1007_s00362-021-01258-9
    DOI: 10.1007/s00362-021-01258-9
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    References listed on IDEAS

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