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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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    1. Chen, S. X., 1994. "Empirical Likelihood Confidence Intervals for Linear Regression Coefficients," Journal of Multivariate Analysis, Elsevier, vol. 49(1), pages 24-40, April.
    2. Lai, T. L. & Ying, Z. L. & Zheng, Z. K., 1995. "Asymptotic Normality of a Class of Adaptive Statistics with Applications to Synthetic Data Methods for Censored Regression," Journal of Multivariate Analysis, Elsevier, vol. 52(2), pages 259-279, February.
    3. Hamilton, Scott A. & Truong, Young K., 1997. "Local Linear Estimation in Partly Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 1-19, January.
    4. Song Chen, 1993. "On the accuracy of empirical likelihood confidence regions for linear regression model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(4), pages 621-637, December.
    5. Gianfranco Adimari, 1997. "Empirical Likelihood Type Confidence Intervals Under Random Censorship," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 447-466, September.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Guo-Liang Fan & Han-Ying Liang & Zhen-Sheng Huang, 2012. "Empirical likelihood for partially time-varying coefficient models with dependent observations," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 71-84.
    5. 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.
    6. Qin, Gengsheng & Zhao, Yichuan, 2007. "Empirical likelihood inference for the mean residual life under random censorship," Statistics & Probability Letters, Elsevier, vol. 77(5), pages 549-557, March.
    7. 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 123-142, November.
    8. 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.
    9. 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.
    10. 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.
    11. Xue, Liu-Gen & Zhu, Lixing, 2006. "Empirical likelihood for single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1295-1312, July.
    12. 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.

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