Physical Sciences and Mathematics Commons^™

Nonparametric Estimation Of The Survival Function Based On Censored Data With Additional Observations From The Residual Distribution, Paul Kvam, Harshinder Singh, Ram C. Tiwari

Department of Math & Statistics Faculty Publications

We derive the nonparametric maximum likelihood estimator (NPMLE) of the distribution of the test items using a random, right-censored sample combined with an additional right-censored, residual-lifetime sample in which only lifetimes past a known, fixed time are collected. This framework is suited for samples for which individual test data are combined with left-truncated and randomly censored data from an operating environment. The NPMLE of the survival function using the combined sample is identical to the Kaplan-Meier product-limit estimator only up to the time at which the test items corresponding to the residual sample were known to survive. The limiting distribution …