Nonparametric Estimation of a Survivorship Function with Doubly Censored Data

Abstract A simple iterative procedure is proposed for obtaining estimates of a response time distribution when some of the data are censored on the left and some on the right. The procedure is based on the product-limit method of Kaplan and Meier [15], and it also uses the idea of self-consistency due to Efron [8]. Under fairly general assumptions, the method is shown to yield unique consistent maximum likelihood estimators. Asymptotic expressions for their variances and covariances are derived and an extension to the case of arbitrary censoring is suggested.

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