Estimation of total time on test transforms and lorenz curves under random censorship
- 1 January 1987
- journal article
- research article
- Published by Taylor & Francis in Statistics
- Vol. 18 (1) , 77-97
- https://doi.org/10.1080/02331888708801993
Abstract
We initiate a nonparametric large sample estimation theory of total time on test transforms and LORENZ curves under random censorship from the right. We introduce appropriate functional estimators for these functions based on teh product-limit estimator and its quantile function and develop strong uniform consistency results and weak convergence theorems in the form of weak approximations by sequences of appropriate copies of the limiting GAUSSian processes. Our main technical tools are the CHIBISOV-O'REILLY theorems for the uniform product-limit and product-limit quantile processes which we establish here. These are of independent interest.Keywords
This publication has 14 references indexed in Scilit:
- Weighted Empirical and Quantile ProcessesThe Annals of Probability, 1986
- Strong approximations of the quantile process of the product-limit estimatorJournal of Multivariate Analysis, 1985
- The rate of strong uniform consistency for the product-limit estimatorProbability Theory and Related Fields, 1983
- Large Sample Behaviour of the Product-Limit Estimator on the Whole LineThe Annals of Statistics, 1983
- Characterization of Nonparametric Classes of Life DistributionsThe Annals of Probability, 1980
- Convergence theorems for empirical Lorenz curves and their inversesAdvances in Applied Probability, 1977
- Life expectancy under random censorshipStochastic Processes and their Applications, 1977
- Applications of Characterizations in the Area of Goodness of FitPublished by Springer Nature ,1975
- A Large Sample Study of the Life Table and Product Limit Estimates Under Random CensorshipThe Annals of Statistics, 1974
- Nonparametric Estimation from Incomplete ObservationsJournal of the American Statistical Association, 1958