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Stochastic integrals of empirical-type processes with applications to censored regression

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  • Lai, Tze Leung
  • Ying, Zhiliang

Abstract

Motivated by the analysis of linear rank estimators and the Buckley-James nonparametric EM estimator in censored regression models, we study herein the asymptotic properties of stochastic integrals of certain two-parameter empirical processes. Applications of these results on empirical processes and their stochastic integrals to the asymptotic analysis of censored regression estimators are also given.

Suggested Citation

  • Lai, Tze Leung & Ying, Zhiliang, 1988. "Stochastic integrals of empirical-type processes with applications to censored regression," Journal of Multivariate Analysis, Elsevier, vol. 27(2), pages 334-358, November.
    • Handle: RePEc:eee:jmvana:v:27:y:1988:i:2:p:334-358
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    Citations

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    Cited by:

    1. Tianqing Liu & Xiaohui Yuan, 2020. "Empirical likelihood-based weighted rank regression with missing covariates," Statistical Papers, Springer, vol. 61(2), pages 697-725, April.
    2. Yichuan Zhao & Song Yang, 2008. "Empirical likelihood inference for censored median regression with weighted empirical hazard functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(2), pages 441-457, June.
    3. Yijian Huang & Limin Peng, 2009. "Accelerated Recurrence Time Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 636-648, December.
    4. Ying Ding & Bin Nan, 2015. "Estimating Mean Survival Time: When is it Possible?," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 397-413, June.
    5. Seung-Hwan Lee, 2010. "Confidence intervals for the regression parameter based on weighted log-rank estimating functions," Computational Statistics, Springer, vol. 25(3), pages 429-440, September.
    6. Zhao, Puying & Haziza, David & Wu, Changbao, 2020. "Survey weighted estimating equation inference with nuisance functionals," Journal of Econometrics, Elsevier, vol. 216(2), pages 516-536.
    7. Ruosha Li & Limin Peng, 2011. "Quantile Regression for Left-Truncated Semicompeting Risks Data," Biometrics, The International Biometric Society, vol. 67(3), pages 701-710, September.
    8. Gongjun Xu & Tony Sit & Lan Wang & Chiung-Yu Huang, 2017. "Estimation and Inference of Quantile Regression for Survival Data Under Biased Sampling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1571-1586, October.
    9. Seung-Hwan Lee, 2016. "On the estimators and tests for the semiparametric hazards regression model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(4), pages 531-546, October.
    10. Yan, Xiaodong & Wang, Hongni & Wang, Wei & Xie, Jinhan & Ren, Yanyan & Wang, Xinjun, 2021. "Optimal model averaging forecasting in high-dimensional survival analysis," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1147-1155.
    11. Yuxue Jin & Tze Leung Lai, 2017. "A new approach to regression analysis of censored competing-risks data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(4), pages 605-625, October.
    12. Meredith Goldwasser & Lu Tian & L. J. Wei, 2004. "Statistical Inference for Infinite Dimensional Parameters Via Asymptotically Pivotal Estimating Functions," Harvard University Biostatistics Working Paper Series 1007, Berkeley Electronic Press.

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