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On Self-Normalization For Censored Dependent Data

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  • Yinxiao Huang
  • Stanislav Volgushev
  • Xiaofeng Shao

Abstract

type="main" xml:id="jtsa12096-abs-0001"> This article is concerned with confidence interval construction for functionals of the survival distribution for censored dependent data. We adopt the recently developed self-normalization approach (Shao, 2010), which does not involve consistent estimation of the asymptotic variance, as implicitly used in the blockwise empirical likelihood approach of El Ghouch et al. (2011). We also provide a rigorous asymptotic theory to derive the limiting distribution of the self-normalized quantity for a wide range of parameters. Additionally, finite-sample properties of the self-normalization-based intervals are carefully examined, and a comparison with the empirical likelihood-based counterparts is made.

Suggested Citation

  • Yinxiao Huang & Stanislav Volgushev & Xiaofeng Shao, 2015. "On Self-Normalization For Censored Dependent Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(1), pages 109-124, January.
    • Handle: RePEc:bla:jtsera:v:36:y:2015:i:1:p:109-124
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    File URL: http://hdl.handle.net/10.1111/jtsa.12096
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    References listed on IDEAS

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    1. Andreas Hagemann, 2014. "Stochastic equicontinuity in nonlinear time series models," Econometrics Journal, Royal Economic Society, vol. 17(1), pages 188-196, February.
    2. Xiaofeng Shao, 2010. "A self‐normalized approach to confidence interval construction in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 343-366, June.
    3. Lobato I. N., 2001. "Testing That a Dependent Process Is Uncorrelated," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1066-1076, September.
    4. Xiaofeng Shao, 2010. "Corrigendum: A self‐normalized approach to confidence interval construction in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 695-696, November.
    5. Zhou Zhou & Xiaofeng Shao, 2013. "Inference for linear models with dependent errors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 323-343, March.
    6. El Ghouch, Anouar & Van Keilegom, Ingrid & McKeague, Ian W., 2011. "Empirical Likelihood Confidence Intervals For Dependent Duration Data," Econometric Theory, Cambridge University Press, vol. 27(1), pages 178-198, February.
    7. Cai, Zongwu & Roussas, George G., 1998. "Kaplan-Meier Estimator under Association," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 318-348, November.
    8. Ying, Z. & Wei, L. J., 1994. "The Kaplan-Meier Estimate for Dependent Failure Time Observations," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 17-29, July.
    9. Cai, Zongwu, 1998. "Asymptotic properties of Kaplan-Meier estimator for censored dependent data," Statistics & Probability Letters, Elsevier, vol. 37(4), pages 381-389, March.
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    Cited by:

    1. Sun, Jiajing & Hong, Yongmiao & Linton, Oliver & Zhao, Xiaolu, 2022. "Adjusted-range self-normalized confidence interval construction for censored dependent data," Economics Letters, Elsevier, vol. 220(C).
    2. Bai, Shuyang & Taqqu, Murad S. & Zhang, Ting, 2016. "A unified approach to self-normalized block sampling," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2465-2493.

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