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Statistical inference based on non-smooth estimating functions

Author

Listed:
  • L. Tian
  • J. Liu
  • Y. Zhao
  • L. J. Wei

Abstract

When the estimating function for a vector of parameters is not smooth, it is often rather difficult, if not impossible, to obtain a consistent estimator by solving the corresponding estimating equation using standard numerical techniques. In this paper, we propose a simple inference procedure via the importance sampling technique, which provides a consistent root of the estimating equation and also an approximation to its distribution without solving any equations or involving nonparametric function estimates. The new proposal is illustrated and evaluated via two extensive examples with real and simulated datasets. Copyright 2004, Oxford University Press.

Suggested Citation

  • L. Tian & J. Liu & Y. Zhao & L. J. Wei, 2004. "Statistical inference based on non-smooth estimating functions," Biometrika, Biometrika Trust, vol. 91(4), pages 943-954, December.
    • Handle: RePEc:oup:biomet:v:91:y:2004:i:4:p:943-954
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    File URL: http://hdl.handle.net/10.1093/biomet/91.4.943
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    Cited by:

    1. Jian Zhang & Faming Liang, 2008. "Convergence of stochastic approximation algorithms under irregular conditions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 62(3), pages 393-403, August.
    2. Zhouping Li & Jinfeng Xu & Wang Zhou, 2016. "On Nonsmooth Estimating Functions via Jackknife Empirical Likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 49-69, March.
    3. Yijian Huang, 2013. "Fast Censored Linear Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 789-806, December.
    4. Zhang, Jiajia & Peng, Yingwei, 2007. "An alternative estimation method for the accelerated failure time frailty model," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4413-4423, May.
    5. Chaohua Dong & Jiti Gao & Bin Peng & Yundong Tu, 2023. "Smoothing the Nonsmoothness," Papers 2309.16348, arXiv.org.
    6. Larry F. León & Ray Lin & Keaven M. Anderson, 2020. "On Weighted Log-Rank Combination Tests and Companion Cox Model Estimators," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(2), pages 225-245, July.

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