论文标题
泊松过程的二阶渐近效率
Second order asymptotic efficiency for a Poisson process
论文作者
论文摘要
当其强度函数周期性时，我们考虑了对不均匀泊松过程的平均功能估计的问题。对于平均综合平方误差（MISE），所有估计器都有经典的下限，而经验平均函数则具有下限，因此它渐近地有效。遵循Golubev和Levit的工作思想，我们比较了渐近效率的估计器，并提出了一个估计器，该估计值是渐近效率的二阶。遵循Pinsker的想法，对Sobolev椭圆形的二阶效率进行了。
We consider the problem of the estimation of the mean function of an inhomogeneous Poisson process when its intensity function is periodic. For the mean integrated squared error (MISE) there is a classical lower bound for all estimators and the empirical mean function attains that lower bound, thus it is asymptotically efficient. Following the ideas of the work by Golubev and Levit, we compare asymptotically efficient estimators and propose an estimator which is second order asymptotically efficient. Second order efficiency is done over Sobolev ellipsoids, following the idea of Pinsker.
