Asymptotic equivalence of estimating a Poisson intensity and a positive diffusion drift
Asymptotic equivalence of estimating a Poisson intensity and a positive diffusion drift
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估计泊松强度和正扩散漂移的渐近等价
DOI：
10.1214/aos/1028674840
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
M. Nussbaum
中科院分区：
文献类型：
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作者：
V. Genon‐Catalot;C. Larédo;M. Nussbaum
本文考虑一个具有正漂移密度的小变量扩散模型。我们调查高斯和泊松近似这个模型。在渐近等价的意义上的实验，它表明，观察的扩散过程，直到它的第一次击中时间的水平1是一个自然的模型的漂移密度的推断的目的。扩散模型可以通过收集水平交叉时间来离散化，用于水平的均匀网格。随机时间增量是渐近充分的，并且服从独立数据的非参数回归模型。然后使用这种解耦来建立单位间隔上高斯白色噪声信号和泊松强度模型的渐进等效性。以及一个i.i.d.当扩散漂移函数f是概率密度时的模型。作为应用，我们找到了估计超范数损失扩散漂移密度的精确渐近极大极小常数。
We consider a diffusion model of small variable type with positive drift density varying in a nonparametric set. We investigate Gaussian and Poisson approximations to this model. In the sense of asymptotic equivalence of experiments, it is shown that observation of the diffusion process until its first hitting time of level one is a natural model for the purpose of inference of the drift density. The diffusion model can be discretized by the collection of level crossing times for a uniform grid of levels. The random time increments are asymptotically sufficient and obey a nonparametric regression model with independent data. This decoupling is then used to establish asymptotic equivalence to Gaussian signal-in-white noise and Poisson intensity models on the unit interval. and also to an i.i.d. model when the diffusion drift function f is a probability density. As an application, we find the exact asymptotic minimax constant for estimating the diffusion drift density with sup-norm loss.