Adaptive estimation of the intensity of inhomogeneous Poisson processes via concentration inequalities
Adaptive estimation of the intensity of inhomogeneous Poisson processes via concentration inequalities
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通过浓度不等式自适应估计非均匀泊松过程的强度
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
Chyong
中科院分区：
文献类型：
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作者：
A. Barron;Chyong
本文建立了非齐次Poisson过程强度的惩罚投影估计的预言不等式。因此，我们研究了惩罚投影估计的自适应性质。首先，我们提供了下界的极大极小风险的各种光滑的强度，然后我们证明了我们的估计达到这些下界的一些常数。得到预言不等式的关键工具是Poisson过程积分泛函上界的新的浓度不等式，它类似于经验过程的Talagrand不等式.
In this paper, we establish oracle inequalities for penalized projection estimators of the intensity of an inhomogeneous Poisson process. We study consequently the adaptive properties of penalized projection estimators. At first we provide lower bounds for the minimax risk over various sets of smoothness for the intensity and then we prove that our estimators achieve these lower bounds up to some constants. The crucial tools to obtain the oracle inequalities are new concentration inequalities for suprema of integral functionals of Poisson processes which are analogous to Talagrand’s inequalities for empirical processes.