ABSTRACT In this paper, we propose a new strategy of estimation for the survival function S, associated to a survival time subject to interval censoring case 2. Our method is based on a least squares contrast of regression type with parameters corresponding to the coefficients of the development of S on an orthonormal basis. We obtain a collection of projection estimators where the dimension of the projection space has to be adequately chosen via a model selection procedure. For compactly supported bases, we obtain adaptive results leading to general nonparametric rates. However, our results can be used for non-compactly supported bases, a true novelty in regression setting, and we use specifically the Laguerre basis which is -supported and thus well suited when non-negative random variables are involved in the model. Simulation results comparing our proposal with previous strategies show that it works well in a very general context. A real dataset is considered to illustrate the methodology.

中文翻译：

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受区间删失情况 2 约束的数据的非参数生存函数估计

摘要 在本文中，我们提出了一种新的生存函数 S 估计策略，与受区间删失情况 2 相关的生存时间。我们的方法基于回归类型的最小二乘对比，参数对应于S 在正交基础上的发展。我们获得了一组投影估计器，其中必须通过模型选择程序充分选择投影空间的维度。对于紧凑支持的基础，我们获得了导致一般非参数率的自适应结果。然而，我们的结果可用于非紧支持基，这是回归设置中的真正新颖之处，我们特别使用了支持的 Laguerre 基，因此非常适合模型中涉及非负随机变量的情况。将我们的提议与以前的策略进行比较的模拟结果表明，它在非常普遍的情况下运行良好。考虑一个真实的数据集来说明该方法。