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Least product relative error estimation

Author

Listed:
  • Chen, Kani
  • Lin, Yuanyuan
  • Wang, Zhanfeng
  • Ying, Zhiliang

Abstract

A least product relative error criterion is proposed for multiplicative regression models. It is invariant under scale transformation of the outcome and covariates. In addition, the objective function is smooth and convex, resulting in a simple and uniquely defined estimator of the regression parameter. It is shown that the estimator is asymptotically normal and that the simple plug-in variance estimation is valid. Simulation results confirm that the proposed method performs well. An application to body fat calculation is presented to illustrate the new method.

Suggested Citation

  • Chen, Kani & Lin, Yuanyuan & Wang, Zhanfeng & Ying, Zhiliang, 2016. "Least product relative error estimation," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 91-98.
    • Handle: RePEc:eee:jmvana:v:144:y:2016:i:c:p:91-98
    DOI: 10.1016/j.jmva.2015.10.017
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    References listed on IDEAS

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    1. Chen, Kani & Guo, Shaojun & Lin, Yuanyuan & Ying, Zhiliang, 2010. "Least Absolute Relative Error Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1104-1112.
    2. Kani Chen & Zhiliang Ying & Hong Zhang & Lincheng Zhao, 2008. "Analysis of least absolute deviation," Biometrika, Biometrika Trust, vol. 95(1), pages 107-122.
    3. Park, Heungsun & Stefanski, L. A., 1998. "Relative-error prediction," Statistics & Probability Letters, Elsevier, vol. 40(3), pages 227-236, October.
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    Citations

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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. 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.
    3. Hao, Meiling & Lin, Yunyuan & Zhao, Xingqiu, 2016. "A relative error-based approach for variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 250-262.
    4. 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.
    5. 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.
    6. Tianzhen Wang & Haixiang Zhang, 2022. "Optimal subsampling for multiplicative regression with massive data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(4), pages 418-449, November.
    7. Zhanfeng Wang & Zhuojian Chen & Zimu Chen, 2018. "H-relative error estimation for multiplicative regression model with random effect," Computational Statistics, Springer, vol. 33(2), pages 623-638, June.
    8. Jun Zhang & Junpeng Zhu & Yan Zhou & Xia Cui & Tao Lu, 2020. "Multiplicative regression models with distortion measurement errors," Statistical Papers, Springer, vol. 61(5), pages 2031-2057, October.
    9. Junmin Liu & Deli Zhu & Luoyao Yu & Xuehu Zhu, 2023. "Specification testing of partially linear single-index models: a groupwise dimension reduction-based adaptive-to-model approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 232-262, March.
    10. 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.
    11. 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.
    12. Ayub, Kanwal & Song, Weixing & Shi, Jianhong, 2022. "Extrapolation estimation in parametric regression models with measurement error," Computational Statistics & Data Analysis, Elsevier, vol. 172(C).
    13. 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.

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