IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v97y2006i7p1586-1599.html
   My bibliography  Save this article

Empirical likelihood inference for linear transformation models

Author

Listed:
  • Lu, Wenbin
  • Liang, Yu

Abstract

Empirical likelihood inference is developed for censored survival data under the linear transformation models, which generalize Cox's [Regression models and life tables (with Discussion), J. Roy. Statist. Soc. Ser. B 34 (1972) 187-220] proportional hazards model. We show that the limiting distribution of the empirical likelihood ratio is a weighted sum of standard chi-squared distribution. Empirical likelihood ratio tests for the regression parameters with and without covariate adjustments are also derived. Simulation studies suggest that the empirical likelihood ratio tests are more accurate (under the null hypothesis) and powerful (under the alternative hypothesis) than the normal approximation based tests of Chen et al. [Semiparametric of transformation models with censored data, Biometrika 89 (2002) 659-668] when the model is different from the proportional hazards model and the proportion of censoring is high.

Suggested Citation

  • Lu, Wenbin & Liang, Yu, 2006. "Empirical likelihood inference for linear transformation models," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1586-1599, August.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:7:p:1586-1599
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(05)00161-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Qin, Gengsheng & Tsao, Min, 2003. "Empirical likelihood inference for median regression models for censored survival data," Journal of Multivariate Analysis, Elsevier, vol. 85(2), pages 416-430, May.
    2. A. N. Pettitt, 1984. "Proportional Odds Models for Survival Data and Estimates Using Ranks," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(2), pages 169-175, June.
    3. Chen, S. X., 1994. "Empirical Likelihood Confidence Intervals for Linear Regression Coefficients," Journal of Multivariate Analysis, Elsevier, vol. 49(1), pages 24-40, April.
    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. Kani Chen, 2002. "Semiparametric analysis of transformation models with censored data," Biometrika, Biometrika Trust, vol. 89(3), pages 659-668, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ming Zheng & Wen Yu, 2013. "Empirical likelihood method for multivariate Cox regression," Computational Statistics, Springer, vol. 28(3), pages 1241-1267, June.
    2. Clelia Di Serio & Yosef Rinott & Marco Scarsini, 2009. "Simpson's Paradox in Survival Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 463-480, September.
    3. Zhao, Yichuan, 2010. "Semiparametric inference for transformation models via empirical likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1846-1858, September.
    4. Wen Yu & Yunting Sun & Ming Zheng, 2011. "Empirical likelihood method for linear transformation models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 331-346, April.
    5. Bravo, Francesco, 2009. "Two-step generalised empirical likelihood inference for semiparametric models," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1412-1431, August.
    6. Yu, Xue & Zhao, Yichuan, 2019. "Empirical likelihood inference for semi-parametric transformation models with length-biased sampling," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 115-125.
    7. Tong Tong Wu & Gang Li & Chengyong Tang, 2015. "Empirical Likelihood for Censored Linear Regression and Variable Selection," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 798-812, September.
    8. Xue Yu & Yichuan Zhao, 2019. "Jackknife empirical likelihood inference for the accelerated failure time model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 269-288, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhao, Yichuan & Chen, Feiming, 2008. "Empirical likelihood inference for censored median regression model via nonparametric kernel estimation," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 215-231, February.
    2. Zhao, Yichuan, 2010. "Semiparametric inference for transformation models via empirical likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1846-1858, September.
    3. Pao-sheng Shen & Yi Liu, 2019. "Pseudo maximum likelihood estimation for the Cox model with doubly truncated data," Statistical Papers, Springer, vol. 60(4), pages 1207-1224, August.
    4. Francesco Bravo, "undated". "Empirical likelihood specification testing in linear regression models," Discussion Papers 00/28, Department of Economics, University of York.
    5. Tan, Xin Lu, 2019. "Optimal estimation of slope vector in high-dimensional linear transformation models," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 179-204.
    6. Liang, Hua & Su, Haiyan & Zou, Guohua, 2008. "Confidence intervals for a common mean with missing data with applications in an AIDS study," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 546-553, December.
    7. Huang, Bin & Wang, Qihua, 2010. "Semiparametric analysis based on weighted estimating equations for transformation models with missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2078-2090, October.
    8. Jing, Bing-Yi, 1995. "Two-sample empirical likelihood method," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 315-319, September.
    9. Bruce Brown & Song Chen, 1998. "Combined and Least Squares Empirical Likelihood," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(4), pages 697-714, December.
    10. Wang, Qihua & Tong, Xingwei & Sun, Liuquan, 2012. "Exploring the varying covariate effects in proportional odds models with censored data," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 168-189.
    11. Jianbo Li & Minggao Gu & Tao Hu, 2012. "General partially linear varying-coefficient transformation models for ranking data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(7), pages 1475-1488, January.
    12. Liu, Yukun & Zou, Changliang & Zhang, Runchu, 2008. "Empirical likelihood for the two-sample mean problem," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 548-556, April.
    13. 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.
    14. Wang, Qihua & Wang, Jane-Ling, 2001. "Inference for the Mean Difference in the Two-Sample Random Censorship Model," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 295-315, November.
    15. Wang, Qi-Hua & Li, Gang, 2002. "Empirical Likelihood Semiparametric Regression Analysis under Random Censorship," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 469-486, November.
    16. Ying Qing Chen & Nan Hu & Su-Chun Cheng & Philippa Musoke & Lue Ping Zhao, 2012. "Estimating Regression Parameters in an Extended Proportional Odds Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 318-330, March.
    17. Guo-Liang Fan & Han-Ying Liang & Jiang-Feng Wang, 2013. "Empirical likelihood for heteroscedastic partially linear errors-in-variables model with α-mixing errors," Statistical Papers, Springer, vol. 54(1), pages 85-112, February.
    18. 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.
    19. Hu, Xuemei & Wang, Zhizhong & Zhao, Zhiwei, 2009. "Empirical likelihood for semiparametric varying-coefficient partially linear errors-in-variables models," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1044-1052, April.
    20. Cui, Hengjian & Chen, Song Xi, 2003. "Empirical likelihood confidence region for parameter in the errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 101-115, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:97:y:2006:i:7:p:1586-1599. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.