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Censored Partial Linear Models and Empirical Likelihood

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  • Qin, Gengsheng
  • Jing, Bing-Yi

Abstract

Consider the partial linear model Yi=X[tau]i[beta]+g(Ti)+[var epsilon]i, i=1, ..., n, where [beta] is a p-1 unknown parameter vector, g is an unknown function, Xi's are p-1 observable covariates, Ti's are other observable covariates in [0, 1], and Yi's are the response variables. In this paper, we shall consider the problem of estimating [beta] and g and study their properties when the response variables Yi are subject to random censoring. First, the least square estimators for [beta] and kernel regression estimator for g are proposed and their asymptotic properties are investigated. Second, we shall apply the empirical likelihood method to the censored partial linear model. In particular, an empirical log-likelihood ratio for [beta] is proposed and shown to have a limiting distribution of a weighted sum of independent chi-square distributions, which can be used to construct an approximate confidence region for [beta]. Some simulation studies are conducted to compare the empirical likelihood and normal approximation-based method.

Suggested Citation

  • Qin, Gengsheng & Jing, Bing-Yi, 2001. "Censored Partial Linear Models and Empirical Likelihood," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 37-61, July.
    • Handle: RePEc:eee:jmvana:v:78:y:2001:i:1:p:37-61
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    References listed on IDEAS

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    3. Yongcheng Qi, 2010. "On the tail index of a heavy tailed distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(2), pages 277-298, April.
    4. Jonker Marianne & Van der Vaart Aad, 2014. "On the Correction of the Asymptotic Distribution of the Likelihood Ratio Statistic If Nuisance Parameters Are Estimated Based on an External Source," The International Journal of Biostatistics, De Gruyter, vol. 10(2), pages 1-20, November.
    5. Otsu, Taisuke & Takahata, Keisuke & Xu, Mengshan, 2023. "Empirical likelihood inference for monotone index model," LSE Research Online Documents on Economics 118123, London School of Economics and Political Science, LSE Library.
    6. Xue, Liu-Gen & Zhu, Lixing, 2006. "Empirical likelihood for single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1295-1312, July.
    7. Hua Liang & Yongsong Qin & Xinyu Zhang & David Ruppert, 2009. "Empirical Likelihood‐Based Inferences for Generalized Partially Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 433-443, September.
    8. Moral-Arce, Ignacio & Rodríguez-Póo, Juan M. & Sperlich, Stefan, 2011. "Low dimensional semiparametric estimation in a censored regression model," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 118-129, January.
    9. Huang, Zhensheng & Pang, Zhen, 2012. "Corrected empirical likelihood inference for right-censored partially linear single-index model," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 276-284.
    10. Tang, Linjun & Zhou, Zhangong & Wu, Changchun, 2013. "Testing the linear errors-in-variables model with randomly censored data," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 875-884.
    11. Gengsheng Qin & Xiao-Hua Zhou, 2006. "Empirical Likelihood Inference for the Area under the ROC Curve," Biometrics, The International Biometric Society, vol. 62(2), pages 613-622, June.
    12. Yongli Sang, 2021. "A Jackknife Empirical Likelihood Approach for Testing the Homogeneity of K Variances," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(7), pages 1025-1048, October.

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