On minimum distance estimation in two-sample scale problem with right censoring
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The estimation of the treatment effect in the two-sample problem with right censoring is of interest in survival analysis. In this paper we consider the scale change model in which a specific treatment extends the life of the patient, in the sense that the lifetime is multiplied by a certain scale factor. For the Koziol-Green (K-G) sub-model of the right censoring model, this research establishes large-sample properties of the minimum Z/2-distance estimator of the scale parameter, similar to that studied in Koul and Yang (1989) for the general right censoring model. The maximum likelihood estimator (MLE) for the survival function under the K-G model is used in the minimum L2-distance estimation of the scale parameter rather than the product limit estimator (PLE) of Kaplan and Meier (1958) as used in Koul and Yang (1989). Several properties of the estimator such as consistency and asymptotic normality are established. A representation of the estimator that facilitates its computation is derived. Furthermore, it is shown that the minimum L2-distance estimator using the MLE of the survival function is asymptotically more efficient than that using the PLE of the survival function under the specified K-G sub-model.