Nonparametric estimation of a distribution with type I bias with applications to competing risks

References

• Yanagimoto , T. and Sibuya , M. 1972 . Tests of symmetry on a one dimensional distribution against positive biasedness . Annals of the Institute of Mathematics , 24 : 423 – 434 .
   Web of Science ®Google Scholar
• Dykstra , R. , Kochar , S. and Robertson , T. 1995 . Likelihood ratio test for symmetry against one sided alternatives . Annals Institute of Mathematics , 47 : 719 – 730 .
   Web of Science ®Google Scholar
• Robertson , T. , Wright , T. and Dykstra , R. 1988 . Order Restricted Statistical Inference , New York : Wiley .
   Google Scholar
• Rojo , J. 1995 . On the weak convergence of certain estimators of stochastically ordered survival functions . Journal of Nonparametric Statistics , 4 : 349 – 369 .
   Google Scholar
• Rojo , J. 2004 . On the estimation of survival functions under a stochastic order constraint . IMS LNMS , 44
   Google Scholar
• Shorack , G. and Wellner , J. A. 1986 . Empirical Processes with Applications to Statistics , New York : Wiley .
   Google Scholar
• Brillinger , D. R. 1962 . A note on the convergence rate of the mean . Biometrika , 49 : 574 – 576 .
   Web of Science ®Google Scholar
• Chung , K. L. 1974 . A Course in Probability Theory , (2nd edn) , New York : Academic Press .
   Google Scholar
• Billingsley , P. 1968 . Convergence of Probability Measures , New York : Wiley .
   Google Scholar
• Rojo , J. and Ma , Z. 1996 . On the estimation of stochastically ordered survival functions . Journal of Statistical Computations and Simulations , 55 : 1 – 21 .
   Web of Science ®Google Scholar
• Breslow , N. and Crowley , J. 1974 . A large sample study of the life table and product limit estimate under random censorship . Annals of Statistics , 2 : 437 – 453 .
   Web of Science ®Google Scholar
• Stone , C. 1963 . Weak convergence of stochastic processes defined on a semifinite time interval . Proceedings American Mathmatical Society , 14 : 694 – 696 .
   Google Scholar
• Lindvall , T. 1973 . Weak convergence of probability measures and random functions in the space D[0, ∞) . Journal of Applied Probability , 10 : 109 – 121 .
   Web of Science ®Google Scholar
• Fleming , T. R. and Harrington , D. P. 1991 . Counting Processes and Survival Analysis , New York : Wiley .
   Google Scholar
• Lin , D. Y. 1997 . Non-parametric inference for cumulative incidence functions in competing risks studies . Statistics in Medicine , 16 : 901 – 910 .
   PubMed Web of Science ®Google Scholar
• Carriere , K. C. and Kochar , S. C. 2000 . Comparing sub-survival functions in a competing risks model . Lifetime Data Analysis , 6 : 85 – 97 .
   PubMed Web of Science ®Google Scholar
• Hoel , D. G. 1972 . A representation of mortality data by competing risks . Biometrics , 65 : 475 – 488 .
   Web of Science ®Google Scholar