Review on Goodness of Fit Tests for Ergodic Diffusion Processes by Different Sampling Schemes
Review on Goodness of Fit Tests for Ergodic Diffusion Processes by Different Sampling Schemes
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不同抽样方案遍历扩散过程拟合优度检验综述
DOI：
10.1111/j.1468-0300.2010.00221.x
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Y. Nishiyama
中科院分区：
文献类型：
--
作者：
I. Negri;Y. Nishiyama
我们回顾了关于一维遍历扩散的漂移系数的拟合优度检验的一些最新结果，其中扩散系数是一个令人讨厌的函数，但是是估计的。使用连续观察情况的理论，我们首先提出基于过程的确定性离散时间观察的测试。然后我们还提出了一种基于空间中离散观察到的数据的测试，即所谓的滴答时间采样方案。在两种抽样方案中，检验的极限分布是标准布朗运动的上界，因此检验是渐近分布自由的。在任何固定替代方案下，测试也是一致的。
We review some recent results on goodness of fit test for the drift coefficient of a one-dimensional ergodic diffusion, where the diffusion coefficient is a nuisance function which however is estimated. Using a theory for the continuous observation case, we first present a test based on deterministic discrete time observations of the process. Then we also propose a test based on the data observed discretely in space, that is, the so-called tick time sample scheme. In both sampling schemes the limit distribution of the test is the supremum of the standard Brownian motion, thus the test is asymptotically distribution free. The tests are also consistent under any fixed alternatives.