Maximum Likelihood Estimator for Semiparametric Transformation Model under General Censorship

Abstract

In a semiparametric transformation model, an increasing transformation of the survival time is linearly related to a covariate Z with an error distribution ε . In other words, the survival time T has the property that (T) =−θz + ε given Z = z , where  is an unknown extended real-valued function on R and θ is an unknown constant in R^d . An observation is said to be censored by a general censorship scheme if there are random intervals which, when the observation falls inside them, would hide it. In such cases we get the censoring interval instead of the actual observation. In this paper we consider maximum likelihood estimation of the transformation function α and the regression coefficient θ when the survival time data are subjected to general censorship.