Adjusted empirical likelihood for varying coefficient partially linear models with censored data. (English) Zbl 1267.62061
Summary: By constructing an adjusted auxiliary vector ingeniously, we propose an adjusted empirical likelihood ratio function for the parametric components of varying coefficient partially linear models with censored data. It is shown that its limiting distribution is standard central chi-squared. Then the confidence intervals for the parametric components are constructed. A simulation study and a real data analysis are undertaken to assess the finite sample performance of the proposed method.
MSC:
62G08 | Nonparametric regression and quantile regression |
62J05 | Linear regression; mixed models |
62N01 | Censored data models |
62G05 | Nonparametric estimation |
62H12 | Estimation in multivariate analysis |
62F25 | Parametric tolerance and confidence regions |
65C60 | Computational problems in statistics (MSC2010) |
References:
[1] | Q. Wang and Z. Zheng, “Asymptotic properties for the semiparametric regression model with randomly censored data,” Science in China A, vol. 40, no. 9, pp. 945-957, 1997. · Zbl 0902.62051 · doi:10.1007/BF02878674 |
[2] | Q. H. Wang and G. Li, “Empirical likelihood semiparametric regression analysis under random censorship,” Journal of Multivariate Analysis, vol. 83, no. 2, pp. 469-486, 2002. · Zbl 1024.62015 · doi:10.1006/jmva.2001.2060 |
[3] | Y. P. Yang, L. G. Xue, and W. H. Cheng, “An empirical likelihood method in a partially linear single-index model with right censored data,” Acta Mathematica Sinica, vol. 28, no. 5, pp. 1041-1060, 2012. · Zbl 1284.62243 · doi:10.1007/s10114-011-9157-0 |
[4] | X. Lu and T. L. Cheng, “Randomly censored partially linear single-index models,” Journal of Multivariate Analysis, vol. 98, no. 10, pp. 1895-1922, 2007. · Zbl 1139.62056 · doi:10.1016/j.jmva.2006.11.008 |
[5] | Q. Wang and L. Xue, “Statistical inference in partially-varying-coefficient single-index model,” Journal of Multivariate Analysis, vol. 102, no. 1, pp. 1-19, 2011. · Zbl 1206.62113 · doi:10.1016/j.jmva.2010.07.005 |
[6] | Z. Huang, “Empirical likelihood-based inference in varying-coefficient single-index models,” Journal of the Korean Statistical Society, vol. 40, no. 2, pp. 205-215, 2011. · Zbl 1296.62086 · doi:10.1016/j.jkss.2010.09.005 |
[7] | J. Fan and T. Huang, “Profile likelihood inferences on semiparametric varying-coefficient partially linear models,” Bernoulli, vol. 11, no. 6, pp. 1031-1057, 2005. · Zbl 1098.62077 · doi:10.3150/bj/1137421639 |
[8] | W. Zhang, S. Y. Lee, and X. Song, “Local polynomial fitting in semivarying coefficient model,” Journal of Multivariate Analysis, vol. 82, no. 1, pp. 166-188, 2002. · Zbl 0995.62038 · doi:10.1006/jmva.2001.2012 |
[9] | A. B. Owen, “Empirical likelihood ratio confidence regions,” Annals of Statistics, vol. 18, no. 1, pp. 90-120, 1990. · Zbl 0712.62040 · doi:10.1214/aos/1176347494 |
[10] | L. Xue, “Empirical likelihood local polynomial regression analysis of clustered data,” Scandinavian Journal of Statistics, vol. 37, no. 4, pp. 644-663, 2010. · Zbl 1226.62042 · doi:10.1111/j.1467-9469.2009.00677.x |
[11] | Y. P. Yang, L. G. Xue, and W. H. Cheng, “Empirical likelihood for a partially linear model with covariate data missing at random,” Journal of Statistical Planning and Inference, vol. 139, no. 12, pp. 4143-4153, 2009. · Zbl 1183.62068 · doi:10.1016/j.jspi.2009.05.046 |
[12] | X. Luo, Y. Li, Y. Ma, and Y. Zhou, “Varying-coefficient partially linear models with censored data,” Acta Mathematica Scientia, vol. 26, pp. 79-92, 2010. |
[13] | T. R. Fleming and D. P. Harrington, Counting Processes and Survival Analysis, John Wiley and Sons, New York, NY, USA, 2005. · Zbl 1079.62093 |
[14] | R. Jiang and W. M. Qian, “Generalized likelihood ratio tests for varying-coefficient models with censored data,” Open Journal of Statistics, vol. 1, no. 1, pp. 19-23, 2011. · doi:10.4236/ojs.2011.11003 |
[15] | Y. P. Mack and B. W. Silverman, “Weak and strong uniform consistency of kernel regression estimates,” Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 61, no. 3, pp. 405-415, 1982. · Zbl 0495.62046 · doi:10.1007/BF00539840 |
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