关于聚合泊松观测的参数估计

IF 0.5 Q3 MATHEMATICS Armenian Journal of Mathematics Pub Date : 2019-04-26 DOI:10.52737/18291163-2019.11.5-1-13

Elhadji Ousseynouu Accrachi, Cherif Ahmat Tidiane Aidara, A. S. Dabye

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引用次数: 0

摘要

我们考虑了通过非齐次泊松过程的观测来估计参数的问题。该过程的强度函数被认为是关于未知参数的光滑函数。我们在一致观测的基础上提出了一个卡方统计量，并在此统计量的帮助下定义了一个最小卡方估计。我们证明了估计量是一致的和渐近正态的。我们讨论了所得结果的可能推广。

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On Parameter Estimation by Aggregated Poisson Observations

We consider the problem of parameter estimation by the observations of inhomogeneous Poisson processes. The intensity function of the process is supposed to be a smooth function with respect to the unknown parameter. We propose a Chi-square statistic on the base of agregated observations and we define a Minimum Chi-square Estimator with the help of this statistics. We show this that estimator is consistent and asymptotically normal. We discuss possible generalizations of the obtained results.

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