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Asymptotic Normality of a Class of Adaptive Statistics with Applications to Synthetic Data Methods for Censored Regression

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  • Lai, T. L.
  • Ying, Z. L.
  • Zheng, Z. K.

Abstract

Motivated by regression analysis of censored survival data, we develop herein a general asymptotic distribution theory for estimators defined by estimating equations of the form [summation operator]ni=1[xi] (wi, [theta], Gn) = 0, in which wi represents observed data, [theta] is an unknown parameter to be estimated, and Gn represents an estimate of some unknown underlying distribution. This general theory is used to establish asymptotic normality of synthetic least squares estimates in censored regression models and to evaluate the covariance matrices of the limiting normal distributions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:52:y:1995:i:2:p:259-279
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    Cited by:

    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. Lu, Xuewen & Burke, M.D., 2005. "Censored multiple regression by the method of average derivatives," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 182-205, July.
    3. 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.
    4. 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.
    5. Wanrong Liu & Xuewen Lu, 2009. "Weighted least squares method for censored linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(7), pages 787-799.
    6. Debbarh, Mohammed & Viallon, Vivian, 2008. "Testing additivity in nonparametric regression under random censorship," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2584-2591, November.
    7. Jin, Zhezhen & He, Wenqing, 2016. "Local linear regression on correlated survival data," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 285-294.
    8. Zhou, Mai, 1999. "Regression analysis with censored data: Extensions of Koul-Susarla-Van Ryzin approach," Statistics & Probability Letters, Elsevier, vol. 41(3), pages 229-236, February.
    9. Lu, Xuewen, 2010. "Asymptotic distributions of two "synthetic data" estimators for censored single-index models," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 999-1015, April.
    10. Bao, Yanchun & He, Shuyuan & Mei, Changlin, 2007. "The Koul-Susarla-Van Ryzin and weighted least squares estimates for censored linear regression model: A comparative study," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6488-6497, August.
    11. Zhensheng Huang, 2012. "Empirical likelihood for varying-coefficient single-index model with right-censored data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(1), pages 55-71, January.
    12. 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.
    13. Gutknecht, Daniel, 2011. "Nonclassical Measurement Error in a Nonlinear (Duration) Model," Economic Research Papers 270763, University of Warwick - Department of Economics.
    14. Lu, Xuewen & Cheng, Tsung-Lin, 2007. "Randomly censored partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1895-1922, November.

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