论文标题
关于SDE延迟的多步估计
On Multi-step Estimation of Delay for SDE
论文作者
论文摘要
我们考虑了通过观察几个SDE的解决方案的延迟估计问题。众所周知，这些模型的MLE是一致且渐近正常的，但似然比函数不是可区分的W.R.T.参数以及MLE的数值计算具有一定的困难。我们提出了一步和两步的MLE，其计算没有此类问题，并渐近地提供了与MLE相当的估计值。这些结构以两个或三个步骤实现。首先，我们构建了一致且渐近地正常的初步估计器，但在渐近效率上不高。然后，我们使用这些估计器和修改的Fisher得分设备来获得一步和两步的MLE。我们认为它的数值实现要简单得多。引入了随机的全受仪表方程，并讨论了相关的统计问题。
We consider the problem of delay estimation by the observations of the solutions of several SDEs. It is known that the MLE for these models are consistent and asymptotically normal, but the likelihood ratio functions are not differentiable w.r.t. parameter and therefore numerical calculation of the MLEs has certain difficulties. We propose One-step and Two-step MLE, whose calculation has no such problems and provide estimator asymptotically equivalent to the MLE. These constructions are realized in two or three steps. First we construct preliminary estimators which are consistent and asymptotically normal, but not asymptotically efficient. Then we use these estimators and modified Fisher-score device to obtain One-step and Two-step MLEs. We suppose that its numerical realization is much more simple. Stochastic Pantograph equation is introduced and related statistical problems are discussed.
