In this paper the problem of one dimensional parameter estimation is considered in the case where observations are coming from inhomogeneous Poisson processes. The method of moments estimation is studied and its stochastic expansion is obtained. This stochastic expansion is then used to obtain the expansion of the moments of the estimator and the expansion of the distribution function. The stochastic expansion, the expansion of the moments and the expansion of distribution function are non asymptotic in nature. Several examples are presented to illustrate the theoretical results.

中文翻译：

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在 Poisson 观测的情况下 MME 的非渐近展开

在本文中，一维参数估计的问题被考虑在观察来自非齐次泊松过程的情况下。研究了矩估计的方法，得到了它的随机展开式。然后使用该随机扩展来获得估计器矩的扩展和分布函数的扩展。随机展开、矩展开和分布函数展开本质上是非渐近的。举几个例子来说明理论结果。