This paper presents a general methodology for nonparametric estimation of a function s related to a nonnegative real random variable X, under a constraint of type \(s(0)=c\). When a projection estimator of the target function is available, we explain how to modify it in order to obtain an estimator which satisfies the constraint. We extend risk bounds from the initial to the new estimator, and propose and study adaptive procedures for both estimators. The example of cumulative distribution function estimation illustrates the method for two different models: the multiplicative noise model (\(Y=XU\) is observed, with U following a uniform distribution) and the additive noise model \((Y=X+V\) is observed where V is a nonnegative nuisance variable with known density).

本文提出了一种在类型\（s（0）= c \）的约束下用于与非负实随机变量X相关的函数的非参数估计的通用方法。当目标函数的投影估计量可用时，我们将说明如何对其进行修改以便获得满足约束的估计量。我们将风险范围从初始估算器扩展到新估算器，并针对这两个估算器提出并研究自适应程序。累积分布函数估计的示例说明了两种不同模型的方法：乘法噪声模型（观察到\（Y = XU \），U遵循均匀分布）和加性噪声模型\（（Y = X + V \）观察到其中V是具有已知密度的非负扰动变量）。