A completely nonparametric method for the estimation of mixture cure models is proposed. A nonparametric estimator of the incidence is extensively studied and a nonparametric estimator of the latency is presented. These estimators, which are based on the Beran estimator of the conditional survival function, are proved to be the local maximum likelihood estimators. An i.i.d. representation is obtained for the nonparametric incidence estimator. As a consequence, an asymptotically optimal bandwidth is found. Moreover, a bootstrap bandwidth selection method for the nonparametric incidence estimator is proposed. The introduced nonparametric estimators are compared with existing semiparametric approaches in a simulation study, in which the performance of the bootstrap bandwidth selector is also assessed. Finally, the method is applied to a database of colorectal cancer from the University Hospital of A Coru\~na (CHUAC).

翻译：本文提出了一种完全非参数的混合治愈模型估计方法。我们深入研究了发病率的非参数估计量，并提出了潜伏期的非参数估计量。这些基于条件生存函数的Beran估计量，被证明是局部最大似然估计量。获得了非参数发病率估计量的独立同分布表示，并由此推导出渐近最优带宽。此外，我们还提出了一种针对非参数发病率估计量的自助法带宽选择方法。通过模拟研究，将所提出的非参数估计量与现有半参数方法进行了比较，并评估了自助法带宽选择器的性能。最后，将该方法应用于拉科鲁尼亚大学医院（CHUAC）的结直肠癌数据库。