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摘要翻译：
本文研究了满足某种结构假设的多元函数的自适应估计问题。我们提出了一种新的估计方法，它同时适应未知结构和底层函数的平滑性。结构自适应问题被表述为从给定的估计量集合中进行选择的问题。我们提出了一个一般的选择规则，并建立了任意$\rl_p$--损失下的全局oracle不等式。将这些结果应用于加性多指标模型的自适应估计。
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英文标题：
《Structural adaptation via $L_p$-norm oracle inequalities》
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作者：
A. Goldenhsluger and O. Lepski
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
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.
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PDF链接：
https://arxiv.org/pdf/704.2492
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