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Jackknife empirical likelihood tests for error distributions in regression models

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  • Feng, Huijun
  • Peng, Liang

Abstract

Regression models are commonly used to model the relationship between responses and covariates. For testing the error distribution, some classical test statistics such as Kolmogorov–Smirnov test and Cramér–von-Mises test suffer from the complicated limiting distribution due to the plug-in estimate for the unknown parameters. Hence some ad hoc procedure such as bootstrap method is needed to obtain critical points. Recently, Khmaladze and Koul (2004) [7] have proposed an asymptotically distribution free test via some Martingale transforms. However, the calculation of such a test becomes quite involved, which usually requires numeric integration when the Cramér–von-Mises type of test is employed. In this paper we propose a novel jackknife empirical likelihood method which is easy to compute and has a chi-square limit so that critical values are ready at hand. A simulation study confirms that the new test has an accurate size and is powerful too.

Suggested Citation

  • Feng, Huijun & Peng, Liang, 2012. "Jackknife empirical likelihood tests for error distributions in regression models," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 63-75.
    • Handle: RePEc:eee:jmvana:v:112:y:2012:i:c:p:63-75
    DOI: 10.1016/j.jmva.2012.05.018
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    References listed on IDEAS

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    1. Jing, Bing-Yi & Yuan, Junqing & Zhou, Wang, 2009. "Jackknife Empirical Likelihood," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1224-1232.
    2. Gong, Yun & Peng, Liang & Qi, Yongcheng, 2010. "Smoothed jackknife empirical likelihood method for ROC curve," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1520-1531, July.
    3. Liang Peng & Yongcheng Qi, 2010. "Smoothed jackknife empirical likelihood method for tail copulas," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 514-536, November.
    4. Koul, Hira L. & Sakhanenko, Lyudmila, 2005. "Goodness-of-fit testing in regression: A finite sample comparison of bootstrap methodology and Khmaladze transformation," Statistics & Probability Letters, Elsevier, vol. 74(3), pages 290-302, October.
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    Cited by:

    1. Xiaohui Liu & Qihua Wang & Yi Liu, 2017. "A consistent jackknife empirical likelihood test for distribution functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 249-269, April.
    2. Yongli Sang & Xin Dang & Yichuan Zhao, 2020. "Depth-based weighted jackknife empirical likelihood for non-smooth U-structure equations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 573-598, June.
    3. Ai-Ai Liu & Han-Ying Liang, 2017. "Jackknife empirical likelihood of error variance in partially linear varying-coefficient errors-in-variables models," Statistical Papers, Springer, vol. 58(1), pages 95-122, March.
    4. Zhang, Zhigang & Zhao, Yichuan, 2013. "Empirical likelihood for linear transformation models with interval-censored failure time data," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 398-409.
    5. Xiaohui Yuan & Huixian Li & Tianqing Liu, 2021. "Empirical likelihood inference for rank regression with doubly truncated data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 25-73, March.

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