On asymptotically distribution free tests with parametric hypothesis for ergodic diffusion processes
On asymptotically distribution free tests with parametric hypothesis for ergodic diffusion processes
复制标题
遍历扩散过程参数假设的渐近分布自由检验
DOI：
10.1007/s11203-014-9096-3
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Y. Kutoyants
中科院分区：
文献类型：
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作者：
M. Kleptsyna;Y. Kutoyants
考虑了用遍历扩散过程的观测值构造渐近分布自由检验的问题。假定在基本假设下，趋势系数依赖于有限维参数，研究了cram<s:1> -von Mises型统计量。底层统计量取决于局部时间估计量与不变密度的偏差，参数由最大似然估计量代替。我们提出了一个线性变换，使检验统计量收敛到维纳过程的一个积分。因此，基于该统计量的检验是渐近无分布的。
We consider the problem of the construction of the asymptotically distribution free test by the observations of ergodic diffusion process. It is supposed that under the basic hypothesis the trend coefficient depends on a finite-dimensional parameter and we study the Cramér-von Mises type statistics. The underlying statistics depends on the deviation of the local time estimator from the invariant density with parameter replaced by the maximum likelihood estimator. We propose a linear transformation which yields the convergence of the test statistics to an integral of the Wiener process. Therefore the test based on this statistics is asymptotically distribution free.