Estimation and application in log-Fréchet regression model using censored data

  • Authors

    • Hanan Alamoudi King Abdualaziz University
    • Salwa‎ Mousa‎ King Abdualaziz University
    • Lamya Baharith King Abdualaziz University
    2017-03-18
    https://doi.org/10.14419/ijasp.v5i1.7221
  • Fréchet Distribution, Regression Model, Censored Data, Maximum Likelihood, Jackknife Method, Residual Analysis.
  • This article introduces a new location-scale regression model based on a log-Fréchet distribution. Maximum likelihood and Jackknife methods are used to estimate the new model parameters for censored data. Martingale and deviance residuals are obtained to check model assumptions, data validity, and detect outliers. Moreover, global influence is used to detect influential observations. Monte Carlo simulation study is provided to compare the performance of the maximum likelihood and jackknife estimators for different sample sizes and censoring percentages. The empirical distribution of the martingale and deviance residuals of the proposed model is examined. A real lifetime heart transplant data is analyzed under the log-Fréchet regression model to illustrate the satisfactory results of the proposed model.

  • References

    1. [1] J.F. Lawless,Statistical models and methods for lifetime data. 2th Ed, John Wiley and Sons, New Jersey. 2003.

      [2] G.O. Silva, E. M. Ortega, V. G. Cancho, M. L. Barreto. Log-Burr XII regression models with censored data. Computational Statistics and Data Analysis 52(7) (2008) 3820-3842. https://doi.org/10.1016/j.csda.2008.01.003.

      [3] J.M. Carrasco, E.M. Ortega,G.A. Paula, Log-modified Weibull regression models with censored data: Sensitivity and residual analysis. Computational Statistics and Data Analysis 52(8) (2008) 4021-4039. https://doi.org/10.1016/j.csda.2008.01.027.

      [4] E.M. Ortega, G.M. Cordeiro, J.M. Carrasco, The log-generalized modified Weibull regression model. Brazilian Journal of Probability and Statistics0 (00) (2009) 1-29.

      [5] E.M. Hashimoto, E.M. Ortega, V.G. Cancho, G.M. Cordeiro, The log-exponentiated Weibull regression model for interval-censored data. Computational Statistics and Data Analysis54 (4) (2009) 1017-1035. https://doi.org/10.1016/j.csda.2009.10.014.

      [6] G.O. Silva, E.M. Ortega, V.G. Cancho, Log-Weibull extended regression model: estimation, sensitivity and residual analysis. Statistical Methodology7 (6) (2010) 614-631. https://doi.org/10.1016/j.stamet.2010.05.004.

      [7] E.M. Hashimoto, E.M. Ortega, G.M. Cordeiro, M.L. Barreto, The Log-Burr XII Regression Model for Grouped Survival Data. Journal of biopharmaceutical statistics 22(1) (2012) 141-159. https://doi.org/10.1080/10543406.2010.509527.

      [8] J.N.d.Cruz, E.M. Ortega, G.M. Cordeiro, The log-odd log-logistic Weibull regression model: modelling, estimation, influence diagnostics and residual analysis. Journal of Statistical Computation and Simulation 86(8) (2016) 1-23. https://doi.org/10.1080/00949655.2015.1071376.

      [9] R.R. Pescim, E.M. Ortega, G.M. Cordeiro, M. Alizadeh, A new log-location regression model: estimation, influence diagnostics and residual analysis. Journal of Applied Statistics (2016) 1-20.

      [10] S.Kotz,S. Nadarajah, Extreme value distributions: theory and applications, World Scientific,London, 2000. https://doi.org/10.1142/p191.

      [11] R.D. Cook, Detection of influential observation in linear regression. Technometrics (1977) 15-18.

      [12] R.G. Miller, An unbalanced jackknife. The Annals of statistics2 (5) (1974) 880-891. https://doi.org/10.1214/aos/1176342811.

      [13] D.Tu, J. Shao, The Jackknife and bootstrap, Springer-Verlag, New York, 1995.

      [14] H. Abdi, L. Williams, Jackknife. Encyclopedia of Research Design, Thousand Oaks, CA: Sage, (2010) 1-10.

      [15] S. Sahinler,D. Topuz, Bootstrap and jackknife resampling algorithms for estimation of regression parameters. Journal of Applied Quantitative Methods2 (2) (2007) 188-199.

      [16] Z.Y. Algamal, K.B. Rasheed, Re-sampling in Linear Regression Model Using Jackknife and Bootstrap. Iraqi Journal of Statistical Science18 (2010) 59-73.

      [17] R. Christensen, L.M. Pearson, W. Johnson, Case-deletion diagnostics for mixed models. Technometrics 34(1) (1992) 38-45. https://doi.org/10.2307/1269550.

      [18] A.Davison,C.-L. Tsai, Regression model diagnostics. International Statistical Review60 (3) (1992) 337-353. https://doi.org/10.2307/1403682.

      [19] F.-C.Xie,B.-C. Wei, Diagnostics analysis for log-Birnbaum–Saunders regression models. Computational Statistics and Data Analysis51 (9) (2007a) 4692-4706. https://doi.org/10.1016/j.csda.2006.08.030.

      [20] F.-C. Xie,B.-C. Wei, Diagnostics analysis in censored generalized Poisson regression model. Journal of Statistical Computation and Simulation 77(8) (2007b) 695-708. https://doi.org/10.1080/10629360600581316.

      [21] D. Collett, Modelling survival data in medical research, CRC press, London, 2003

      [22] W.E.Barlow,R.L. Prentice, Residuals for Relative Risk Regression, in Biometrika Biometrika Trust (1988) 65-74.

      [23] T.M. Therneau, P.M. Grambsch, T.R. Fleming, Martingale-based residuals for survival models. Biometrika 77(1) (1990) 147-160. https://doi.org/10.1093/biomet/77.1.147.

      [24] J.D.Kalbfleisch,R.L. Prentice, The statistical analysis of failure time data. 2thEd, John Wiley & Sons,New Jersey, 2002. https://doi.org/10.1002/9781118032985.

      [25] Y.Zhao, A.H. Lee, K. K. Yau, G. J. McLachlan, Assessing the adequacy of Weibull survival models: a simulated envelope approach. Journal of Applied Statistics 38(10) (2011) 2089-2097. https://doi.org/10.1080/02664763.2010.545115.

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