Goodness of fit test for ergodic diffusion processes
Goodness of fit test for ergodic diffusion processes
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遍历扩散过程的拟合优度检验
DOI：
10.1007/s10463-007-0162-0
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发表时间：
2006
影响因子：
1
通讯作者：
Y. Nishiyama
中科院分区：
文献类型：
--
作者：
I. Negri;Y. Nishiyama
给出了遍历扩散过程漂移系数的拟合优度检验。检验是基于评分的经验过程。在原假设下研究了该检验统计量的弱收敛性，证明了极限过程是连续高斯过程。它的协方差函数的结构允许计算极限分布，它原来是一个标准的布朗运动的函数，因此可以构造精确的拒绝区域。该检验是渐近分布自由的，并且在任何简单的固定替代下都是一致的。
A goodness of fit test for the drift coefficient of an ergodic diffusion process is presented. The test is based on the score marked empirical process. The weak convergence of the proposed test statistic is studied under the null hypothesis and it is proved that the limit process is a continuous Gaussian process. The structure of its covariance function allows to calculate the limit distribution and it turns out that it is a function of a standard Brownian motion and so exact rejection regions can be constructed. The proposed test is asymptotically distribution free and it is consistent under any simple fixed alternative.