We propose a semiparametric estimator of the survival function S (t) = P (T>t) from the censored observation Zi = min {Ti;Ci} and the corresponding indicators Zi =1 (Xi <= Ci), where the independent cencored times Ci are independent of the independent survival times Ti. Our goal is to obtain predictions of the survival probabilities S (t) outside the range of the observed times, that is for t > max{Zi}. The main idea of the proposed approch is to to choose adaptively a threshold u starting from which the predictions of the survival times are still reliable. Below the threshold S (t) is estimated by a completely non-parametric method, such as the Kaplan-Meyer one. Above the threshold a parametric model is proposed - here we use an exponential law. The choice of the threshold u is performed by a sequence of goodness-of-fit tests.