标题： 结构适应通过$L_p$-范数oracle不等式 显示英文标题

标题： Structural adaptation via $L_p$-norm oracle inequalities

摘要： 本文研究了满足某些结构假设的多元函数自适应估计问题。我们提出了一种新的估计程序，能够同时适应未知的结构和底层函数的光滑性。结构适应问题被表述为从给定的估计器集合中选择的问题。我们发展了一般的选择规则，并在任意$\rL_p$--损失下建立了全局oracle不等式。这些结果应用于加性多指标模型的自适应估计。 显示英文摘要

摘要： In this paper we study the problem of adaptive estimation of a multivariate function satisfying some structural assumption. We propose a novel estimation procedure that adapts simultaneously to unknown structure and smoothness of the underlying function. The problem of structural adaptation is stated as the problem of selection from a given collection of estimators. We develop a general selection rule and establish for it global oracle inequalities under arbitrary $\rL_p$--losses. These results are applied for adaptive estimation in the additive multi--index model.