Courses / ActivitiesKaplan-Meier Estimator (K-M)
116
reads
In this lecture, we focus on estimating the survival function of the failure time without any specified distribution assumption. The K-M can be derived as the Nonparametric Maximum Likelihood Estimator (NMLE) or Product Limit (PL) estimator which is the limit of life table estimator. We also can prove K-M estimator is the solution of Self-Consistent (SC) estimation equation and can be computed by the redistribute the mass to the right algorithm. The asymptotic to the normality of the K-M estimator will be proved and asymptotic variance (Greenwood formula) will be derived.
Reading:
1. E.L. Kaplan and P. Meier (1958). Non-parametric estimation from incomplete observations. J. Amer. Statist. Assoc. 53, 457–481, 562–563. (primary reading)
2. B. Efron (1967). The two sample problem with censored data. Proc. 5th Berkeley Symp. Math. Statist. Probab. 4, 851–853. (first half : secondary reading )
3. N.E. Breslow and J.J. Crowley (1974). A large sample study of the life table and product limit estimates under random censorship. Ann. Statist. 2, 437–453. (secondary reading)
4. R.D. Gill (1983), Large sample behavior of the product-limit estimator on the whole line. Ann. Statist. 11, 49–58. (Reading for the Ph.D. students)
reads
Wei-Yann Tsai
2010-06-11
12:30:00 - 14:30:00
405 , Mathematics Research Center Building (ori. New Math. Bldg.)
Lecture 1:In this lecture, we focus on estimating the survival function of the failure time without any specified distribution assumption. The K-M can be derived as the Nonparametric Maximum Likelihood Estimator (NMLE) or Product Limit (PL) estimator which is the limit of life table estimator. We also can prove K-M estimator is the solution of Self-Consistent (SC) estimation equation and can be computed by the redistribute the mass to the right algorithm. The asymptotic to the normality of the K-M estimator will be proved and asymptotic variance (Greenwood formula) will be derived.
Reading:
1. E.L. Kaplan and P. Meier (1958). Non-parametric estimation from incomplete observations. J. Amer. Statist. Assoc. 53, 457–481, 562–563. (primary reading)
2. B. Efron (1967). The two sample problem with censored data. Proc. 5th Berkeley Symp. Math. Statist. Probab. 4, 851–853. (first half : secondary reading )
3. N.E. Breslow and J.J. Crowley (1974). A large sample study of the life table and product limit estimates under random censorship. Ann. Statist. 2, 437–453. (secondary reading)
4. R.D. Gill (1983), Large sample behavior of the product-limit estimator on the whole line. Ann. Statist. 11, 49–58. (Reading for the Ph.D. students)