基于小波强度估计的点过程多分辨率分析和统计阈值
Multiresolution analysis of point processes and statistical thresholding for wavelet-based intensity estimation
摘要：
我们采用小波基的方法来分析点过程和估计的一阶强度下的连续时间设置。一个点过程的多分辨率分析制定激励定义的同质性在不同尺度的分辨率，称为$J$ -th级同质性。此外，还定义了点过程在不同分辨率尺度下的一阶行为的活动，并称之为$L$ -级新息。这两个属性的似然比检验提出了渐近分布提供，即使只有一个实现的点过程进行观察。$L$ -th级创新的测试形成了基于小波的强度函数估计器中阈值系数的统计策略集合的基础。这些阈值策略的表现优于现有的本地硬阈值策略在一系列的模拟场景。
英文摘要：
We take a wavelet based approach to the analysis of point processes and the estimation of the first order intensity under a continuous time setting. A multiresolution analysis of a point process is formulated which motivates the definition of homogeneity at different scales of resolution, termed $J$-th level homogeneity. Further to this, the activity in a point processes' first order behavior at different scales of resolution is also defined and termed $L$-th level innovation. Likelihood ratio tests for both these properties are proposed with asymptotic distributions provided, even when only a single realization of the point process is observed. The test for $L$-th level innovation forms the basis for a collection of statistical strategies for thresholding coefficients in a wavelet based estimator of the intensity function. These thresholding strategies are shown to outperform the existing local hard thresholding strategy on a range of simulation scenarios.
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