Abstract
We fit parametric models to survival data in the case of censoring and (outlier) contamination. To do so, we adapt the robust density power divergence methodology of Basu, Harris, Hjort, and Jones (Biometrika, 85, 549–559, 1998) to the case of censored survival data. Asymptotic properties, simulation performance and application to data are provided.
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References
Basu A., Harris I.R., Hjort N.L., Jones M.C. (1998). Robust and efficient estimation by minimising a density power divergence. Biometrika 85:549–559
Beran R. (1977). Minimum Hellinger distance estimates for parametric models. Annals of Statistics 5:445–463
Cao R., Cuevas A., Fraiman R. (1995). Minimum distance density-based estimation. Computational Statistics and Data Analysis 20: 611–631
Efron B. (1988). Logistic regression, survival analysis, and the Kaplan–Meier curve. Journal of the American Statistical Association 83:414–425
Heathcote C.R. (1977). The integrated squared error estimation of parameters. Biometrika 64:255–264
Hong C., Kim Y. (2001). Automatic selection of the tuning parameter in the minimum density power divergence estimation. Journal of the Korean Statistical Association 30:453–465
Kaplan E.L., Meier P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association 53:457–481
Kullback S., Leibler R.A. (1951). On information and sufficiency. Annals of Mathematical Statistics 22:79–86
Lehmann E.L. (1983). Theory of Point Estimation. Wiley, New York
Miller R.G. (1981). Survival Analysis. Wiley, New York
Peterson A.V. (1977). Expressing the Kaplan–Meier estimator as a function of empirical subsurvival functions. Journal of the American Statistical Association 72:854–858
Reid N. (1981). Influence functions for censored data. Annals of Statistics 9:78–92
Scott D.W. (2001). Parametric statistical modeling by minimum integrated square error. Technometrics 43:274–285
Stute W. (1995). The central limit theorem under random censorship. Annals of Statistics 23:422–439
Stute W., Wang J.L. (1993). The strong law under random censorship. Annals of Statistics 21:1591–1607
Wand M.P., Jones M.P. (1995). Kernel Smoothing. Chapman and Hall, London
Wang J.L. (1995). M-estimators for censored data: strong consistency. Scandinavian Journal of Statistics 22:197–206
Wang J.L. (1999). Asymptotic properties of M-estimators based on estimating equations and censored data. Scandinavian Journal of Statistics 26:297–318
Warwick J., Jones M.C. (2005). Choosing a robustness tuning parameter. Journal of Statistical Computation and Simulation 75:581–588
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Basu, S., Basu, A. & Jones, M.C. Robust and Efficient Parametric Estimation for Censored Survival Data. Ann Inst Stat Math 58, 341–355 (2006). https://doi.org/10.1007/s10463-005-0004-x
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DOI: https://doi.org/10.1007/s10463-005-0004-x