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Empirical likelihood for least absolute relative error regression

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  • Zhouping Li
  • Yuanyuan Lin
  • Guoliang Zhou
  • Wang Zhou

Abstract

Multiplicative regression models are useful for analyzing data with positive responses, such as wages, stock prices and lifetimes, that are particularly common in economic, financial, epidemiological and social studies. Recently, the least absolute relative error (LARE) estimation was proposed to be a useful alternative to the conventional least squares (LS) or least absolute deviation (LAD). However, one may resort to the time-consuming resampling methods for the inference of the LARE estimation. This paper proposes an empirical likelihood approach towards constructing confidence intervals/regions of the regression parameters for the multiplicative models. The major advantage of the proposal is its ability of internal studentizing to avoid density estimation. And it is computationally fast. Simulation studies investigate the effectiveness of the proposed method. An analysis of the body fat data is presented to illustrate the new method. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • Zhouping Li & Yuanyuan Lin & Guoliang Zhou & Wang Zhou, 2014. "Empirical likelihood for least absolute relative error regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 86-99, March.
    • Handle: RePEc:spr:testjl:v:23:y:2014:i:1:p:86-99
    DOI: 10.1007/s11749-013-0343-5
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    References listed on IDEAS

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    1. Song Chen & Ingrid Van Keilegom, 2009. "A review on empirical likelihood methods for regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 415-447, November.
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    5. 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.
    6. Teekens, R & Koerts, J, 1972. "Some Statistical Implications of the Log Transformation of Multiplicative Models," Econometrica, Econometric Society, vol. 40(5), pages 793-819, September.
    7. Song Chen & Ingrid Van Keilegom, 2009. "Rejoinder on: A review on empirical likelihood methods for regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 468-474, November.
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    Cited by:

    1. 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.
    2. Xia, Xiaochao & Liu, Zhi & Yang, Hu, 2016. "Regularized estimation for the least absolute relative error models with a diverging number of covariates," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 104-119.

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