THE STATISTICAL ANALYSIS OF KAPLAN-MEIER INTEGRALS *

Let Fn denote the Kaplan-Meier estimator computed from a sample of possibly censored data, and let f be a given function. In this paper some of the most important properties of the Kaplan-Meier integral f

[1]  Robert Tibshirani,et al.  An Introduction to the Bootstrap , 1994 .

[2]  P. Major,et al.  Strong Embedding of the Estimator of the Distribution Function under Random Censorship , 1988 .

[3]  Winfried Stute,et al.  Strong and weak representations of cumulative hazard function and Kaplan-Meier estimators on increasing sets , 1994 .

[4]  David W. Mauro,et al.  A Combinatoric Approach to the Kaplan-Meier Estimator , 1985 .

[5]  W. Stute,et al.  The strong law under random censorship , 1993 .

[6]  N. Etemadi.  An elementary proof of the strong law of large numbers , 1981 .

[7]  The Natural Duration of Lung Cancer. , 1955, Canadian Medical Association journal.

[8]  G. Shorack.  Asymptotic Normality of Linear Combinations of Functions of Order Statistics , 1969 .

[9]  P. Major,et al.  An approximation of partial sums of independent RV's, and the sample DF. II , 1975 .

[10]  S. Csörgo,et al.  Strong approximations of some biometric estimates under random censorship , 1981 .

[11]  J. Klein,et al.  Statistical Models Based On Counting Process , 1994 .

[12]  Zhiliang Ying,et al.  A note on the asymptotic properties of the product-limit estimator on the whole line , 1989 .

[13]  N. Breslow,et al.  A Large Sample Study of the Life Table and Product Limit Estimates Under Random Censorship , 1974 .

[14]  W. Strawderman.  The Generalized Jackknife Statistic , 1973 .

[15]  J. Neveu,et al.  Discrete Parameter Martingales , 1975 .

[16]  Winfried Stute,et al.  The Bias of Kaplan-Meier Integrals , 1994 .

[17]  R. Gill.  Censoring and stochastic integrals , 1980 .

[18]  R. Gill.  Large Sample Behaviour of the Product-Limit Estimator on the Whole Line , 1983 .

[19]  D. Harrington,et al.  Counting Processes and Survival Analysis , 1991 .

[20]  W. Stute.  Improved estimation under random censorship , 1994 .

[21]  J. V. Ryzin,et al.  LARGE SAMPLE THEORY FOR AN ESTIMATOR OF THE MEAN SURVIVAL TIME FROM CENSORED SAMPLES , 1980 .

[22]  Farhad Mehran,et al.  The Generalized Jackknife Statistic , 1975 .

[23]  M. H. Quenouille.  NOTES ON BIAS IN ESTIMATION , 1956 .

[24]  J. Wellner.  A Heavy Censoring Limit Theorem for the Product Limit Estimator , 1985 .

[25]  A correction to and improvement of ‘Strong approximations of some biometric estimates under random censorship’ , 1988 .

[26]  M. Hollander,et al.  Small-Sample Results for the Kaplan-Meier Estimator , 1982 .

[27]  Richard D. Gill,et al.  Lectures on survival analysis , 1994 .

[28]  W. Stute.  The jackknife estimate of variance of a Kaplan-Meier integral , 1996 .

[29]  K. Singh,et al.  The product-limit estimator and the bootstrap: Some asymptotic representations , 1986 .

[30]  E. Kaplan,et al.  Nonparametric Estimation from Incomplete Observations , 1958 .

[31]  M. Zhou,et al.  Two-sided bias bound of the Kaplan-Meier estimator , 1988 .

[32]  J. O. Irwin,et al.  The standard error of an estimate of expectation of life, with special reference to expectation of tumourless life in experiments with mice , 1949, Journal of Hygiene.

[33]  Donald P. Gaver,et al.  Jackknifing the kaplan-meier survival estimator for censored data: Simulation results and asymptotic analysis , 1983 .

[34]  J. Wellner,et al.  Empirical Processes with Applications to Statistics , 2009 .

[35]  Winfried Stute,et al.  The jackknife estimate of a Kaplan-Meier integral , 1994 .

[36]  Song Yang.  A central limit theorem for functionals of the Kaplan--Meier estimator , 1994 .

[37]  Winfried Stute,et al.  The Central Limit Theorem Under Random Censorship , 1995 .