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A new likelihood approach is proposed for the problem of semiparametric estimation of a conditional distribution or density under censoring. Consistency and asymptotic normality for two versions of the maximum likelihood estimator of the parameter vector in the single index model are proved. The single-index model considered can be seen as a useful tool for credit scoring and estimation of the default probability in credit risk. A data-driven bandwidth selection procedure is proposed. It allows to choose the smoothing parameter involved in our approach. The finite sample performance of the estimators has been studied by simulations, where the new method has been compared with the method proposed by Bouaziz and Lopez (2010) . To the best of our knowledge this is the only existing competitor in this context. The simulation study shows the good behavior of the proposed method.