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Vol. 15 No. 2
julio-diciembre de 2015

ARTICULOS DE INVESTIGACION

Comparison of nonparametric estimators versus parametric for reliability function

https://doi.org/10.19053/1900771X.4246

Published 2015-06-26

  • Javier Ramírez-Montoya

Javier Ramírez-Montoya
Universidad de Sucre,Departamento de Matemáticas y Física, Grupo Investigación en Estadística y Aplicaciones GINESAP.

Abstract

One of the main objectives of the area of realiability is to estimate the function of reliability, where traditionally are used non parametric estimators, being more efficient in sample of big sizes. In this work nonparametric estimators are compared to the reliability function through the mean square error using nonparametric estimators of Kaplan & Meier (1958), Nelson estimator (1969) and Bootstrap applied to Kaplan & Meier and Nelson. The comparison is made considering the parametric estimates, through simulation with different scenarios, times of interest, sizes sample and percentages of censorship, showing that the Bootstrap resampling normal type does not present the best results with Kaplan & Meier. Using Nelson, the 18% was more efficient.

Keywords

bootstrap, reliability, nonparametric estimators.

PDF (Español)

Author Biography

Javier Ramírez-Montoya

Departamento de matemáticas y física, Grupo investigación en estadística y aplicaciones. GINESAP

References

  1. Aalen O. & Johansen S. (1978). An Empirical Transition Matrix for Nonhomogeneus Markov Chains Based on Censored Observations. Scandinavian Journal of Statistics, 5, 141-150.
  2. Akritas M. (1986). Bootstrapping the Kaplan-Meier Estimator. American Statistical Association, 81, 1032-1138.
  3. doi: 10.1080/01621459.1986.10478369
  4. Arrabal, C., Dos Santos, K., Da Rocha, R. Nonaka, R. & Meira, S. (2014). Comparison of resampling method applied to censored data. International Journal of Advanced Statistics and Probability, 2(2), 48-55. doi: 10.14419/ijasp.v2i2.2291
  5. Borgan, ∅. & Liestol, K. (1990). A Note on Confidence Intervals and Bands for the Survival Function Based on Transformations. Scandinavian Journal of Statistics, 17(1), 35-41.
  6. Colosimo, E. & Giolo, S. (2006). Análise de sobrevivencia aplicada, En E. Blucher (ed.). Belem: Universidade Federale do Pará.
  7. Greenwood, M. (1926). The natural duration of cancer. Reports on Public Health and Medical Subjects, 33, 1-26.
  8. Record Number 19272700028
  9. He, P., Kong, G. & Su, Z. (2013). Estimating the survival functions for right-censored and interval-censored data with piecewise constant hazard functions. Contemporary Clinical Trials, 35, 122-127. Doi: http://dx.doi.org/10.1016/j.cct.2013.04.009
  10. Kalbfleisch, J. & Prentice, R. (1980). The statistical analysis of failure time data. New York: Wiley. doi: 10.1002/9781118032985
  11. Kaplan, E. & Meier, P. (1958). Estimation from Incomplete Observations. American Statistical Association, 53, 457-481.
  12. Doi: 10.1080/01621459.1958.10501452
  13. Lawless, J. (2003). Statistical Models and Methods for Lifetime Data. New York: Wiley and Sons. Doi:10.1002/9781118033005.fmatter
  14. Nelson, W. (1969). Hazard plotting for incomplete failure data. Journal of Quality Technology, 61, 27-52.
  15. Nelson, W. (1982). Applied Life Data Analysis, New York: John Wiley Sons. doi: 10.1002/bimj.4710270615
  16. Ramírez, J. (2011). Comparación de intervalos de confianza para la función de supervivencia con censura a derecha. Revista Colombiana de Estadística, 34, 197-209.

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