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Empirical likelihood based modal regression

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Listed:
  • Weihua Zhao
  • Riquan Zhang
  • Yukun Liu
  • Jicai Liu

Abstract

In this paper, we consider how to yield a robust empirical likelihood estimation for regression models. After introducing modal regression, we propose a novel empirical likelihood method based on modal regression estimation equations, which has the merits of both robustness and high inference efficiency compared with the least square based methods. Under some mild conditions, we show that Wilks’ theorem of the proposed empirical likelihood approach continues to hold. Advantages of empirical likelihood modal regression as a nonparametric approach are illustrated by constructing confidence intervals/regions. Two simulation studies and a real data analysis confirm our theoretical findings. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Weihua Zhao & Riquan Zhang & Yukun Liu & Jicai Liu, 2015. "Empirical likelihood based modal regression," Statistical Papers, Springer, vol. 56(2), pages 411-430, May.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:2:p:411-430
    DOI: 10.1007/s00362-014-0588-4
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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. Lee, Myoung-jae, 1989. "Mode regression," Journal of Econometrics, Elsevier, vol. 42(3), pages 337-349, November.
    6. Chuanhua Wei & Yubo Luo & Xizhi Wu, 2012. "Empirical likelihood for partially linear additive errors-in-variables models," Statistical Papers, Springer, vol. 53(2), pages 485-496, May.
    7. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    8. 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. Fayyaz Bahari & Safar Parsi & Mojtaba Ganjali, 2021. "Empirical likelihood inference in general linear model with missing values in response and covariates by MNAR mechanism," Statistical Papers, Springer, vol. 62(2), pages 591-622, April.
    2. Hu Yang & Ning Li & Jing Yang, 2020. "A robust and efficient estimation and variable selection method for partially linear models with large-dimensional covariates," Statistical Papers, Springer, vol. 61(5), pages 1911-1937, October.
    3. Yu Shen & Han-Ying Liang, 2018. "Quantile regression and its empirical likelihood with missing response at random," Statistical Papers, Springer, vol. 59(2), pages 685-707, June.

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