Nonparametric estimation of survival function in the presence of information through functionals

摘要

We are motivated by the reference [5] on nonparametric maximum likelihood estimate (NPMLE) of a lifetime cumulative distribution function (cdf) F on the basis of two independent samples, one of size m from F and the second of size n from G(x), a length biased distribution of F. One can obtain NPMLE of S(x) = 1 — F(x), the Survival Function when G is a suitable functional of F. We obtain NPMLE of 5, when G(t) is known a positive power of F. When power is unknown we propose estimators of the power and F. Based on extensive simulations, performance of estimators, using sup, L1 and L2 norms have been studied.