Estimator selection with respect to Hellinger-type risks
Estimator selection with respect to Hellinger-type risks
复制标题
关于 Hellinger 型风险的估计器选择
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Y. Baraud
中科院分区：
文献类型：
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作者：
Y. Baraud
我们观察一个随机测度N，目的是估计它的强度s。这个统计框架允许同时处理的问题估计的密度，边际的多元分布，平均值的随机向量与非负分量和强度的泊松过程。我们的估计策略是基于估计量的选择。给出了基于N的观测值的s的估计族，考虑到在这些估计族中进行选择，我们提出了一个基于N的选择规则。对估计量的集合几乎不做假设，并且它们相对于观测N的依赖性不需要知道。该过程提供了处理各种问题的可能性，其中包括模型选择，凸聚集和T-估计量的构建，如最近在Birgé（Ann Inst H Poincaré Probab Stat 42（3）：273-325，2006）中研究的那样。为了说明，我们将考虑估计问题，完全变量选择和选择之间的线性估计在可能的非高斯回归设置。
We observe a random measure N and aim at estimating its intensity s. This statistical framework allows to deal simultaneously with the problems of estimating a density, the marginals of a multivariate distribution, the mean of a random vector with nonnegative components and the intensity of a Poisson process. Our estimation strategy is based on estimator selection. Given a family of estimators of s based on the observation of N, we propose a selection rule, based on N as well, in view of selecting among these. Little assumption is made on the collection of estimators and their dependency with respect to the observation N need not be known. The procedure offers the possibility to deal with various problems among which model selection, convex aggregation and construction of T-estimators as studied recently in Birgé (Ann Inst H Poincaré Probab Stat 42(3):273–325, 2006). For illustration, we shall consider the problems of estimation, complete variable selection and selection among linear estimators in possibly non-Gaussian regression settings.