Abstract We consider the problem of the nonparametric estimation in a functional regression model Y = r ( X ) + e , with Y a real random variable response and X representing a functional variable taking values in a semi-metric space. The aim of this note is to find conditions of admissibility of Stein-type estimators of such a model under a class of balanced loss functions. Our method is to compare the risk with that obtained in the case of a quadratic loss.

中文翻译：

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函数回归模型在一些平衡损失函数下的可接受性结果

摘要 我们考虑函数回归模型 Y = r ( X ) + e 中的非参数估计问题，其中 Y 是实数随机变量响应，X 表示函数变量在半度量空间中取值。本笔记的目的是在一类平衡损失函数下找到这种模型的 Stein 型估计量的可接受条件。我们的方法是将风险与在二次损失情况下获得的风险进行比较。