Skip to main content
Log in

On the choice of smoothing parameters for semirecursive nonparametric hazard estimators

  • Article
  • Published:
Journal of Statistical Theory and Practice Aims and scope Submit manuscript

Abstract

In this article we propose an automatic selection of the bandwidth of the semirecursive kernel estimators of the hazard function for uncensored observations. We show that, using the selected bandwidth and a special stepsize, the proposed semirecursive estimators will be quite a bit better than the nonrecursive one in terms of estimation error and much better in terms of computational costs. We corroborated these theoretical results through simulation study and a real earthquake dataset.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Ahmad, I. A. 1976. Uniform strong convergence of the generalized failure rate estimated. Bulletin of Mathematical Statistics 17:77–84.

    MATH  Google Scholar 

  • Altman, N., and C. Leger. 1995. Bandwidth selection for kernel distribution function estimation. Journal of Statistical Planning and Inference 46:195–214.

    Article  MathSciNet  Google Scholar 

  • Bagkavos, D., and P. N. Patil. 2008. Local polynomial fitting in failure rate estimation. IEEE Transactions on Reliability 56:126–63.

    Google Scholar 

  • Bagkavos, D. 2011. Local linear hazard rate estimation and bandwidth selection. Annals of the Institute of Statistical Mathematics 63:1019–46.

    Article  MathSciNet  Google Scholar 

  • Bojanic, R., and E. Seneta. 1973. A unified theory of regularly varying sequences. Mathematische Zeitschrift 134:91–106.

    Article  MathSciNet  Google Scholar 

  • Cheng, M. Y. 1997. Boundary aware estimators of integrated density derivative products. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 59:191–203.

    Article  MathSciNet  Google Scholar 

  • Delaigle, A., and I. Gijbels. 2004. Practical bandwidth selection in deconvolution kernel density estimation. Computational Statistics Data Analysis 45:249–67.

    Article  MathSciNet  Google Scholar 

  • Galambos, J., and E. Seneta. 1973. Regularly varying sequences. Proceedings of the American Mathematical Society 41:110–16.

    Article  MathSciNet  Google Scholar 

  • Mokkadem, A., and M. Pelletier. 2007. A companion for the Kiefer–Wolfowitz–Blum stochastic approximation algorithm. Annals Statistics 35:1749–72.

    Article  MathSciNet  Google Scholar 

  • Mokkadem, A., M. Pelletier, and Y. Slaoui. 2009. The stochastic approximation method for the estimation of a multivariate probability density. Journal of Statistical Planning and Inference 139:2459–78.

    Article  MathSciNet  Google Scholar 

  • Mïler, H. G., and J. L. Wang. 1994. Hazard rate estimation under random censoring with varying kernels and bandwidths. Biometrics 50:61–76.

    Article  MathSciNet  Google Scholar 

  • Murthy, V. K. 1965. Estimation of jumps, reliability and hazard rate. Annals of Statistics 36:1032–40.

    Article  MathSciNet  Google Scholar 

  • Quintela-del-Rio, A., and G. Estévez-Pérez. 2012. Nonparametric kernel distribution function estimation with kerdist: An R package for bandwidth choice and applications. Journal of Statistical Software 50:1–21.

    Article  Google Scholar 

  • Rebora, P., A. Salim, and M. Reilly. 2014. bshazard: A flexible tool for nonparametric smoothing of the hazard function. R Journal 6:114–1221.

    Google Scholar 

  • Silverman, B. W. 1986. Density estimation for statistics and data analysis. London, UK: Chapman and Hall.

    Book  Google Scholar 

  • Slaoui, Y. 2013. Large and moderate principles for recursive kernel density estimators defined by stochastic approximation method. Serdica Mathematical Journal 39:53–82.

    MathSciNet  MATH  Google Scholar 

  • Slaoui, Y. 2014a. Bandwidth selection for recursive kernel density estimators defined by stochastic approximation method. Journal of Probability and Statistics 2014:739640. doi:10.1155/2014/739640.

    Article  MathSciNet  Google Scholar 

  • Slaoui, Y. 2014b. The stochastic approximation method for the estimation of a distribution function. Mathematical Methods of Statistics 23:306–25.

    Article  MathSciNet  Google Scholar 

  • Slaoui, Y. 2015. Plug-in bandwidth selector for recursive kernel regression estimators defined by stochastic approximation method. Statistica Neerlandica 69:483–509.

    Article  MathSciNet  Google Scholar 

  • Slaoui, Y. 2016. Optimal bandwidth selection for semi-recursive kernel regression estimators. Statistics and its Interface 9:375–88.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yousri Slaoui.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Slaoui, Y. On the choice of smoothing parameters for semirecursive nonparametric hazard estimators. J Stat Theory Pract 10, 656–672 (2016). https://doi.org/10.1080/15598608.2016.1214853

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1080/15598608.2016.1214853

Keywords

AMS Subject Classification

Navigation