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Reduced bias nonparametric lifetime density and hazard estimation

Author

Listed:
  • Arthur Berg

    (Penn State College of Medicine)

  • Dimitris Politis

    (University of California)

  • Kagba Suaray

    (California State University Long Beach)

  • Hui Zeng

    (Penn State College of Medicine)

Abstract

Kernel-based nonparametric hazard rate estimation is considered with a special class of infinite-order kernels that achieves favorable bias and mean square error properties. A fully automatic and adaptive implementation of a density and hazard rate estimator is proposed for randomly right censored data. Careful selection of the bandwidth in the proposed estimators yields estimates that are more efficient in terms of overall mean square error performance, and in some cases, a nearly parametric convergence rate is achieved. Additionally, rapidly converging bandwidth estimates are presented for use in second-order kernels to supplement such kernel-based methods in hazard rate estimation. Simulations illustrate the improved accuracy of the proposed estimator against other nonparametric estimators of the density and hazard function. A real data application is also presented on survival data from 13,166 breast carcinoma patients.

Suggested Citation

  • Arthur Berg & Dimitris Politis & Kagba Suaray & Hui Zeng, 2020. "Reduced bias nonparametric lifetime density and hazard estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 704-727, September.
    • Handle: RePEc:spr:testjl:v:29:y:2020:i:3:d:10.1007_s11749-019-00677-z
    DOI: 10.1007/s11749-019-00677-z
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    References listed on IDEAS

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    1. C. Sánchez-Sellero & W. González-Manteiga & R. Cao, 1999. "Bandwidth Selection in Density Estimation with Truncated and Censored Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(1), pages 51-70, March.
    2. Ricardo Cao & Ignacio López-de-Ullibarri, 2007. "Product-type and presmoothed hazard rate estimators with censored data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 355-382, August.
    3. Jacobo de Uña-Álvarez & Luís Meira-Machado, 2015. "Nonparametric estimation of transition probabilities in the non-Markov illness-death model: A comparative study," Biometrics, The International Biometric Society, vol. 71(2), pages 364-375, June.
    4. Gijbels, I. & Wang, J. L., 1993. "Strong Representations of the Survival Function Estimator for Truncated and Censored Data with Applications," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 210-229, November.
    5. Politis, Dimitris N. & Romano, Joseph P., 1999. "Multivariate Density Estimation with General Flat-Top Kernels of Infinite Order," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 1-25, January.
    6. Arthur Berg & Dimitris Politis, 2009. "Higher-order accurate polyspectral estimation with flat-top lag-windows," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(2), pages 477-498, June.
    7. López-de-Ullibarri, Ignacio & Jácome, M. Amalia, 2013. "survPresmooth: An R Package for Presmoothed Estimation in Survival Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 54(i11).
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